This was an incredible week. And before we get into the SpaceX Launch Escape Test, and we've got a little bit of footage from the Boeing Starliner capsule itself, I did want to take a moment to ask you to hit that like, subscribe, and then mash on that notification bell. About 50% of the people who watch this show are not subscribed. And if you hit that subscribe button, maybe we'll be able to hit that 100,000 subscriber mark by the end of 2020. Right now, YouTube says we won't do it till 2021, and I would love to prove them wrong. All right, let's go ahead and get started. Now, for those who don't know, I actually work at SpaceX, but I'm not an official sports person for SpaceX, which means I can't talk about SpaceX. So for that launch abort test, I've got a brand new SpaceX correspondent. So take it away, Ryan. So let's just say, SpaceX News has been kind of hectic this past week, and I originally wrote this segment for release last week, realized that I wouldn't have time to shoot it for last week, and then the in-flight abort test was happening. So let's get right into that. For possibly one of the most exciting Falcon 9 launches this year, the test was a huge success. The naked booster launched at approximately 1530 UTC on January 19th, and the booster being used was B1046, which was the first Block 5 booster to be launched on May 11th of 2018. Now, I do find it quite sad that they did decide to get the booster be destroyed and not store it in a museum somewhere since it was the first Block 5 booster, but it did lead to a very cool-looking fireworks display for all of us to watch. At 86 seconds into flight, the 9 million 1D engines performed a simulated failure, or in other words, they prematurely shut down all of the main engines, which led to the crew dragon capsule automatically triggering an abort as it fired all eight of its Super Draco thrusters, which ignited for eight seconds, allowing the spacecraft to get to a safe distance away from there at this time, destroyed Falcon 9 booster. The spacecraft ditched its unpressurized trunk section, flipped itself around ready for the eight minute coast back down to the Atlantic Ocean. At eight minutes and 57 seconds into flight, the capsule made a safe splashdown, which allowed the recovery teams to swoop in and recover the vehicle. Now that the escape system has been proven to work at Max-Q, which is a period of time when the vehicle is experiencing the most amount of aerodynamic pressure in flight, it's full steam ahead for Demo Mission 2 with astronauts Doug Hurley and Bob Benking later this year. And now, you're gonna see me from about a week ago. While CEO Elon Musk has been dancing around in China with his electric car company, SpaceX haven't been quiet, as in fact they have been increasing their not-so-little-any-more collection of Starlink satellites in Earth orbit with its first 2020 launch of the Falcon 9 at 219 UTC on January 7th. Like the previous Starlink launch, 60 satellites are sent into orbit by the Falcon 9 to expand the constellation of the future high-speed internet provider. However, unlike the previous launch, one of the satellites had a special coating to reduce the albedo of its bodywork. The way that the Starlink satellites are launched means that until they've reached a desired orbit of 550 kilometers, the satellites are closely clustered together and in a low-drag configuration, making them appear more visible to the ground. And it could take anywhere from one to four months before the satellites reach that desired 550 kilometer orbit. Ground-based telescopes and astronomers don't really appreciate bright lights in the sky when they are trying to focus on a certain object in the cosmos. And if SpaceX is going to be launching 60 satellites every two weeks, that means that over 1,000 satellites are going to be in orbit. And that means there will be a lot of light. So as well as doing the experimental coating, SpaceX also provided leading astronomy groups with predictive two-line elements, which is basically a data format that encodes a list of the satellite orbital elements for a given point in time. Using this, they could work out the position and velocity of the satellites so they would know what they could slash couldn't look at with their telescopes, which I think is a pretty good call by SpaceX to try and help out the astronomical community, get the best possible outcome for them, as well as SpaceX. And not being able to see parts of the sky because of a large number of large, bright satellites really isn't a good thing because space telescopes are really expensive. Sometimes aren't even focused properly when you get into orbit, like Hubble. And some take a really long time to launch, like the James Webb Space Telescope. Like seriously, when is that thing launching 2021? Yeah, we need to make these satellites less reflective. Otherwise, we might not even be able to get the super fast global broadband that so many remote places need. Because even though ground observation has discovered so many incredible things in the past, in this day and age, internet connectivity is one of the most essential things in our lives. And I think that if people have the world's knowledge at their fingertips, then this may be a small price to pay for a large A to everybody here on Earth. When most batteries are starting satellites are launched, you have the chance to see a train of them all together. Now, in my opinion, these look really, really cool just to know that then trails of light in the sky can help me connect to the internet. So if you'd like to check when you could see a train of satellites, I'd recommend N2YO.com as they'll let you track latitude, longitude, altitude, velocity, and so many more factors about the satellites. And you can even check, like, you can even check the last Starlink launch. They're still tracking them, it's incredible. And that isn't the only piece of news to Hawthorne-based rocket company brings us this week as the DragonCapture used on the CRS-19 mission, which launched December 5th, safely smashed down in the Pacific Ocean at 1540 UTC on January 7th, which was just a few hours after that Starlink launch. The capture had 3,800 pounds, or 1,724 kilograms of cargo to bring back down to the Earth. This Dragon spacecraft had also been used on the CRS-4 mission in September, 2014, and the CRS-11 mission in June of 2017. Elon Musk has also shared on Twitter the design of the Starlink ground terminals with them being, and I quote, a thin, flat, round UFO on a stick. The terminals will also have motors so they can point to the optimal angle in the sky, and that to install the emergency to plug them in, I'll point them in the sky. He also made it clear that these instructions can be completed in any order. SpaceX is extremely close to launching astronauts to the International Space Station, but let's not forget about Boeing. While we don't know if Boeing will need to redo their uncrewed test flight that happened in late 2019, when I sort of read the tea leaves, it really is sounding like they're not going to need to. And that may be okay. So long as they got enough test data to show that they can keep astronauts and the space station safe. And in my opinion, let's just do this thing. What you've been looking at here is footage from inside Boeing Starliner during this OFT-1 or Orbital Flight Test mission. You can see the very small vibe impact on instrumentation during launch, and also just how smooth that ride looks to be. We get to see the little plush snoopy with an astronaut helmet floating around, their version of Little Earth or a zero G indicator. It's cute, fun, and snoopy has an amazing history with the space program. Then in the end, plasma shoots past the window as the vehicle re-enters the atmosphere. It's an absolutely stunning sight, and I would personally love to see that myself someday. The final little bump you see here at the end is the spacecraft safely touching down on land for the very first time. All in all, it looked like a very successful test. Now it's time for the engineers to look at the data, sharpen their pencils, and make some decisions on the next steps forward. Let's turn our attention over to traffic leaving the Earth with our space traffic report. First up, we have China. A Long March 2D rocket took to the skies on January 14th, 2020 at 02.53 universal time. Aboard, the Earth Observation Satellite Yiling-1. The satellite is part of a planned constellation of imaging satellites that will provide super-wide coverage with a resolution better than one meter and is also capable of high-speed data transmission. And this is going to be a very busy year for China as they're planning on launching 50 times this year up from the 34 that they did last year. Next up is a commercial satellite launch also from China. The solid fuel Qiaos-1A rocket lifted off January 16th at 03.02 universal time. Aboard was a test satellite for Galaxy Space who plans on launching 144 of these in low Earth orbit, which will provide Q-Band, V-Band, and K-A-Band broadband services in the next few years. And finally this week, we have Ariane Space reaching the inky blackness of the cosmos on January 16th, 2105 universal time. The first of their planned 22 launches of 2020. This mission included the UTEL-SET Connect Communication Satellite, as well as the GSAT-30 Direct-to-Home Video Satellite for India. Now let's shift from space traffic to space weather. Dr. Tamatha Scove brings us the latest from our local star. Space weather this week continues to ratchet up in activity. As we switch to our front-side sun, you can see on the 14th blammo right there we had a solar storm launch. Now this storm was Earth-directed, but it really didn't affect us all that much because it was pretty weak. But hey, who cares? It's a new solar storm launch. We haven't seen that since we've been sitting in the solar minimum, so we're very happy about that. Now on top of that, we also had a small active region. This looks like a solar cycle 25 sunspot. It actually was a sunspot for a short moment before it dived back underneath the surface. Oh well, so much for that, but it's still good signs of new activity. Now also we have a coronal hole that's gonna be rotating into the Earth strikes and but it's very small coronal hole, so don't expect a lot from that. Maybe a little aurora at high latitudes. Now switching to our far-side sun, this is the view from stereo. It's kind of looking at the sun from the side. There's not a lot going on, but you do see up in the northeast quadrant you can see an active region rotating into stereo's view. This looks like a solar cycle 25 sunspot as well and you can see it looks like it's actively flaring. So it looks like as this region rotates into Earth view over the next couple of days, we are gonna continue the fun. And now for your Martian Minute. With the Mars 2020 NASA rover launch plan for later this year and manned missions to mine ice on the moon by 2024, the race is on to find habitable places on the red planet for the first human colonists to land. So where will it be? Near water ice deposits of course, but to find ice on Mars shallow enough for the colonists to dig up, not such an easy task until now. In a paper published recently in Geophysical Research Letters, scientists have provided the first map of water ice believed to be as little as two and a half centimeters below the surface. Engineers planning a Martian mission have long known that water ice is a key for any potential landing site because human colonists will have to harvest this ice for drinking water and for making rocket fuel. Using two heat sensitive instruments aboard the Mars Reconnaissance Orbiter, MRO, and the Mars Odyssey spacecraft, scientists have made what is affectionately called a treasure map of Mars. This map shows where water ice could potentially be within the digging ability of ice mining colonists. Using temperature changes on the Martian surface, along with other correlative data, the colored regions on the map reveal a trove of water ice beneath the surface throughout the Martian poles. But the real treasure is the particularly shallow deposits at mid-latitudes, which are ideal for colonists to mine. Sovapiku, the leader author on the study, says, quote, you wouldn't need a backhoe to dig up this ice. You could use a shovel, unquote. Indeed, back in 2008, NASA's Phoenix Lander did exactly that and it even took pictures of the ice it scraped up in the permafrost near the poles. Since then, MRO has taken many images of meteor impacts that have exposed similar ice beneath the surface. So while there are severe limits imposed on possible landing sites for human colonization, some promising possibilities have emerged. Scientists are particularly interested in an area just northwest of Olympus Mons called Arcadia, Planitia, where the water ice is less than 30 centimeters below the surface. Highlighted in the map with an abundance of blue and purple, right now it is the clear winter due to its plentiful sunlight, warmer temperatures, and its generally lower elevation, which provide more atmospheric drag to slow down an incoming spacecraft, perfect for a gentle landing. And speaking of perfect, right now near the equator at Elysian, Planitia, the InSight Lander is enjoying a nice sunny day. Currently, it's a balmy minus 16 degrees Celsius with a low of minus 97 and the winds are out of the South Southeast at 20 meters a second. For more details on this week's space weather, including when and where you can see Aurora and how GPS and radio communications for space traffic is going to fare, come check out my channel or see me at spaceweatherwoman.com. This Space News episode talked a lot about testing for commercial crew. Some of these tests have been great. Some of them have been not so great, but all of them have yielded incredible data.  In fact, 53 years ago, this week, there was an Apollo test you probably never heard of and did not go as expected. Let me paint the picture here. It's January 20th, 1967 and NASA is testing a third stage of their mighty Saturn V rocket, specifically known as the S4B launch vehicle 503. It just rolls right off the tongue. It was built by Douglas Aircraft Company and had one J2 engine on board. This particular stage would never see space. 10 seconds before the simulated ignition of the Saturn V first stage and about eight minutes before the ignition of this specific test article, a weld in one of the helium tanks failed. The resulting release of energy completely destroyed not just the engine and stage, but the actual test stand itself. Yikes. Investigators found that one of the helium storage spheres had been built using the wrong weld material. Now that resulted in a weaker than anticipated tank weld and well, big badaboom. And yes, this video you're watching right now is actually of the S4B interior showing said helium spheres. That's pretty cool. One year, two days later or 52 years ago this week, a Saturn 1B with another S4B second stage launched on Apollo 5, putting the LM1, the first lunar lander to reach space into Earth orbit. It just goes to show that an anomaly in testing doesn't necessarily mean a huge setback for the program as a whole. It's just a data point. And that data point can be used to make your vehicle better and safer. All right, that's our show. I hope you enjoyed it and I wanted to give a huge shout out and thank you to all of the citizens of tomorrow who helped to make this specific episode happen. The people you see on the screen right now they contribute week after week and month after month to the show helping us keep the station on orbit and the lights on. We couldn't do this without you and you all get special content. In 2020, we're trying to bring you even more. Get you better, more awesome rewards, go live more awesome, do anything we can to make this a really compelling offering for you and building you new content week after week. If you'd like to find out how you can help crowdfund the shows of tomorrow, head on over to youtube.com slash T-M-R-O slash join. For those of you waiting for our next live show, we're tentatively planning on one January 25th or 26th. It'll be with Karrion and myself, the first official live show of 2020. We're really excited for it. Now the day job might force us to slide it to the left or right a little bit. So make sure you're subscribed to YouTube so you get that notification in your YouTube stream. It makes all of the difference. I'd like to thank everyone so much for watching. We'll see you next week. And also a first for a U.S. built the Skase Casco. A Skase Casco, everyone. Remember, they're no longer space capsules. They're Skase Cascals.


Hey, what's up, everybody? I wanted to share something that I thought was super duper cool. It's not my work I'm a huge fan of this though. This is amazing. This is the highest resolution ever video of the surface of our Sun You are looking at a tiny little chunk of the surface of the Sun. This is like boiling motion You're seeing this is what we call convection. This is what happens in a pot of water when you boil it This effect in solar and stellar atmospheres was pioneered by the late professor Eric of Bonbatens Who I had the good fortune of getting to work with once in my youth. Each of these cells you're seeing is like the size of Texas So 500 to 1,000 miles across. The resolution is incredible. But what astounds me is the time scale. Look at the clock You're seeing something the size of Texas boil and move and shift in five to ten minutes This is a very small portion of the Sun. Something like 0.01% To draw an analogy this would be like standing back from the earth like a million miles And taking a high-resolution picture of Vermont Now this new movie comes from the Daniel K. Inouye solar telescope Decast, which is this massive four meter diameter telescope Now if you've ever taken a magnifying glass and pointed at the Sun you know that that's collecting a lot of heat So the engineering marvel required to take a 12-foot piece of glass and focus it from the Sun The whole facility is full of like liquid cooling and airflow considerations. On top of that They use what we call adaptive optics, which means they're constantly reshaping the mirror in real time to get this incredibly crispy beautiful image of the Solar surface. It's really astounding. The only thing more amazing than Decast is the story of Daniel K. Inouye himself He was like the first senator and the first representative I think from Hawaii He also spent most of his life with one arm because he was an incredible war hero Please go check out his Wikipedia page that I'll link below it reads like an amazing action film now This is a press release image or video. So it means it's both better and worse than the real data It's better and that it's been cleaned up and smoothed It's worse because the system's not at full capacity yet and by smoothing it You lose a little bit of the fine-skilled detail. Please make the next press release image like a zoom in of a sunspot I cannot wait to see how amazing the detail that Decast gathers this. Forget those wide area all-sky surveys That we're always talking about if you're interested in the big data and data analysis challenges that astronomy has check out the sun


Now that you complete the register, I have posted the link in the chat, if you can't find the link, let me know. Then I can repost the link again. Welcome again to your exam preparation. The purpose of today's session, like I said, is just to go through the question that's part of revision and also preparing you to go write the exam. So it means I'm not doing any explanation of the concept or content. We just going to go through the question and answer the question and look out for tips and tricks in terms of how to answer question and what to look out for. The main purpose is for you, for the preparation, actually not the main purpose for the preparation for you to know that you are ready to go write the exam. You need to find as many as possible different types of questions, especially from the past exam papers. Or you need to go through a trial paper that your lecturer would have given you, especially on the platform or on my UNISA or my module, use that to practice because that will look almost similar to how your exam would look like. Today we're just going to go through some of the questions based on the past question papers. So then I will also tell you what you need to look out for. The other thing I need to mention is that for STA 1610, the structure of your questions for your exam will follow the structure of your study unit. So the first few questions will come from study unit one, followed by study unit two, followed by study unit three, until you get to study unit 11. You have 11 questions, you are writing out of 25 questions. Therefore it means every study unit will have at least two questions. With the exception of very few study units where you might get three questions, study unit one, two and three are almost close and similar to one another, they are linked. So you might find that questions from those that units appears multiple times from question one up until question six. So you just need to know how to identify the questions and be able to pick key elements within the question. Like we've been doing and practicing during the academic session way, you need to make sure that you understand the question, identify the facts given in the question. Then also identify the things that will help you answer the question like the formulas, the tables and so on. And then do the calculation if the question requires you to do the calculation and then look for the answer. Because you're writing a multiple choice question, the other thing that you need to always be aware of. You need to either evaluate every options given of all the statements that you are given to answer the question or they might ask you a question and you need to calculate and find the only one answer from the option. If you need to evaluate the question in the exam, not the same as when you are doing the practices in the exam. So the first question that you evaluate and it answers the question, it is that answer you move on. Unless if you are not sure about your answer, you are not 100% sure that you can evaluate all five statements. But in the exam, you need to be aware of the time because you're writing out of two hours. So be mindful of the time as you evaluate questions. Sooner you get to the answer, move on to the next question and always be prepared and be mindful of that. Okay, with that being said, let's do STA 610. Unless if there are any questions relating to the process of today. So this trial paper that I'm sharing with you, there is also a detailed solution at the end, but I'm not interested in the detailed solution. I'm interested in making sure that you understand the questions and understand how to answer those questions. So I expect you also to talk to me. I don't want the session to be about me. I have been talking since from March, like I said from March or April up until September. So my voice is very tired of me saying things again and again and again. So I expect you now to reflect on things so that I can help you and guide you in terms of answering the questions. So let's look at question number one, which one of the following or which one of this variable is not a quantitative variable. So you need to know what a quantitative variable is. Number one, the number of rings on a person's finger, the height of a person, weight of the person, a person's opinion and about legislation of marijuana, age of the person. So which one of this is not a quantitative. So the key things that you need to look out for is all that. Which one of those one, two, three, four or five. Four. Number four, not a qualitative variable. Question two, the following is a stem and leaf display representing the amount of gasoline purchased in gallons for a sample of 17 cars. Do you still remember a stem and leaf plot is the plot that is ordered in array and it's got the stem and the leaf. And when you read the values, this is not one, five, eight, it is 41, 45, 48. Right. Based on this 17 car sample size on displayed on a stem and leaf plot, which one of the following statement is incorrect. We need to find the statement that is not correct. The range, you need to be calculating what the range is, what the mode is, what is the fifth largest observation and what is the median. And number five, I've already gave you the answer. So do you know what the range is? The range is your highest value minus your lowest value. The mode is the most frequent number. The largest, so you will need to do the count up until you get to the fifth observation and that will be your, sorry, from the bottom. The fifth largest observation is the fifth number from the bottom. So you just need to be able to know which one is that. And then you need to first find the position by using the formula position by using the formula n plus one divided by two where n is the number of observations and divide by two. If your median is on a whole number position. So for example, if it's one, then your median is on position one and you go and read the value that you see. If your median position ends with point five, then you need to take the average where the value of the median position falls between those two values and take the average, meaning add the two values and divide by two. Okay, so because this is a question where we need to validate each statement, so let's go on. What is the range? What is your highest value? 73. 73 and your lowest value? 41. 41, so do the calculation. 73 minus 41. 32. 32, so therefore it means this is correct. What is the mode? Which number appears more than the other numbers? That's the incorrect one because 52 was an appearance. Karim? Karim? Mode in this case will be 52, 65 and 66. The mode, they are 52, 65 and 66 because 52 appears twice, 65 appears twice and 66 appears twice. So this is the incorrect statement, but because we are doing the practice because you will never know in the exam you might need to go and find all the other values. So let's continue. The fifth largest observation, so you need to count, you can count the leaves so that you get to the fifth number and then read out the stem and the leaf of that. So what is the fifth largest observation? Say one, two, three, four, five, which is 56. So that means this is correct. What is the median? So we need to first calculate the position so we know that they are 17 because I don't have to go and count how many they are. They told us in the beginning. So you say 17 plus one divided by two, 18 divided by two is nine. Therefore it means it's on position nine. So you go to your leaf and you count until you get to nine. One, two, three, four, five, six, seven, eight, nine. So it is the median will be 61. And I already told you that the stem and leaf plot is an ordered array or it's data that it's ordered from lowest to highest, which is also known as the ordered array. And that's how you will evaluate every statement. Easy. And so three, a graphical technique applicable to qualitative data is, remember, qualitative data is data that you can put into categories. Which one? One, is it a histogram? Two, is it a stem and leaf plot or display? Three, is it an ogive? Four, is it a data plot? Five, is it a pie chart? Which graphic or which graphical technique or which graph can you use to display data that can be placed into categories, which we call categorical data or qualitative data? One, two, three, four or five. Anyone? Pie chart, it will be a pie chart because a histogram is for numerical values and there are no gaps in between a stem and leaf plot. We just went through a stem and leaf plot. The stem and leaf plot is for numerical values. And ogive, you can develop an ogive from a histogram by just taking the median of the values and the cumulative frequencies because an ogive is your cumulative frequency polygon. And a scatter plot uses two numerical values, your x and y variable. And we use the scatter plot, remember, in study unit 11. So you need to know these things. Okay, question four. The following data represents the number of children in a sample of 11 families. Number of children is numerical value in a sample of 11 families. So it means they're giving you 11 data points. And the size of 11 data points. One, two, three, four, five, six, seven, eight, nine, 10, 11. 11 families. Which one of the following statement is correct? So we're looking for the correct statement. Therefore, it means we need to evaluate all the statements. Number one, the distribution is not symmetric. Therefore, what they are saying is the mean is not equal to the median. That's what you need to evaluate. If the mean and the median are equal, therefore it means the data is symmetric. Number two is the median. We find the position first by using n plus one divided by two and then we'll find the median value. It means before you do that, you need to sort your data from lowest to highest before you can find the median. Your data needs to be sorted. There is only, only the mode is equal to the median. You need to go and check the mode, the most frequent number, the median, you would have found it in number two. Are they equal? So you need to check that only the mean and the median are equal. So when you answer number one, you would be able to answer number four as well, because you need to calculate the mean and you need to find the median. Remember the mean to calculate the mean is the sum of all your values divided by how many we are. The median and the second quartile are not equal. Do you know what the second quartile is in terms of the quarter and do you know what the median is? So if you're not sure about it, the second quarter, you find it by first finding the position of n plus one divided by two to find the mean, the quartile value. And once you get the position, then you go and find the value. The median, you go find the position and once you have the position, then you're going to find the value. So there is no need for you to do any calculation because I've just given you the answer on number five. Okay, so with that, first I will suggest that you sort the data from smallest to highest. Zero is also a number. So I'll give you a few minutes and then you will tell me the numbers. I will write them on here. Are you done writing out the number in order? I don't know. Are you guys saying you can't find the link? Let me post the register again. I've just posted the register again on the chat for those of you who can't find it. Okay, are you done? Give me the numbers in ascending order. Anyone? No one. Okay, zero, zero, zero, one, one, one, two, two, four, four and five. That's how you will write them in ascending order. Now let's answer the question. The mean, can we calculate the mean? If you add all of them, is the sum of all of them? Twenty. Twenty divided by eleven. What is twenty divided by eleven? Lizzie. It's Adele. Hi Adele. May I please ask that students who cannot access the register put their student numbers in the chat, but we need to make sure because of the personal information protection act when students put their student number in the chat that there are a way that other students can also see their student numbers. Yes, I did mention that to them. Okay, thank you. Thank you Lizzie. Thank you Adele. Twenty divided by eleven. Let's keep it to two decimal. One point. One point eight two. One point eight two, okay. Now let's also go and find the median. I'm not going to answer that question. I'm just going to do the calculation and then we'll come back and answer all the questions. The median, we need to first find the position. So let's find the position. So that will be eleven plus one divided by two. Six. Which will be equals to six position. Therefore the median is one. It's one. What is the mode? Let's go find the mode. Zero and one. Zero and one. Okay now let's answer the question. The distribution is not symmetrical. So it means the mean is not equals to the median. Is that true? Our median is one. Our mean is one point eight two. So option one is the correct answer. But we can also go and look at the rest of the questions. So we know that the median is one. So it means that question is incorrect. Only the mode is equals to the median. We know that we've got two modes. So it's also not correct. Only the mean and the median are equal. We just proved that with question number one. That they are not equal. The median and the second quartile are not equal. They are the same. It's one and the same thing, right? So also that's not correct because they are equal because it's the same thing. So you need to be able to know how to answer every question based on the calculations that you have done. In the exam, the minute you get to question number one and you answer number one, you don't have to even worry about the rest of the other question, right? Using the value in number one, calculate the standard deviation. You can either use your calculator by putting your calculator to state mode and capture the information. Or you can use a formula. So your formula will be s is equals to the square root of the sum of your x observation minus the mean squared divided by n minus one, which should be very interesting if you need to answer it in this way. Those who know how to use their calculator to put your calculator to state mode, you can do that. So our first value, we know what the mean is, is 1.8. So zero minus 1.8 to squared s, zero minus 1.8 to squared plus one minus 1.8 to squared plus one minus 1.8 to squared plus until you get to the end, not going to go to the end, five minus 1.8 to squared. And then you divide everything. So don't forget to do two to all the ones and the twos and the fours as well. They in between and we say 11 minus one. I'm going to use a calculator but because I didn't open my calculators online, I'm going to use my actual calculator to put my calculator on state mode. So if you don't know how to use your calculator on this, there are recordings that we shared in the previous sessions that we had when we use our calculator. If you are using Acacia, I can tell you the steps, but you will have to follow what I do. You first need to put your calculator to state mode by pressing the mode button and then pressing the one minus bar. So you will press state and you will do state SD which is button zero and then you will press one for one minus bar and you will have a table with X and to capture the data, you just press zero equal, zero equal, zero equal, one equal, one equal, one equal, two equal, two equal, four equal, four equal and five equal. I hope I have all of them. One, two, three, four, five, six, seven, eight, nine, ten, eleven. Then you will have up until eleven and once you are done, your data is stored on your calculator and then you press AC button which now you are ready to calculate and to calculate, we can even start with the mean.  The mean will be the X bar. If you want to calculate the standard deviation, which is what we are looking for, you just press the AC button and press shift, start again and then press the var again, I think it's button number four and you will press the S X. So on your calculator, it will be S X and when you press the S X and press equal and your answer will be 1.7786 which is the same as in four decimal, it will be 1.7787, which is option two. So that will be, I calculate the whole thing, it will be the square root of 3.16 which is the variance and when I take the square root of the variance, I get 1.778. Long way or short way? On your calculator, using the shortcut using state mode, it's quick and easy to do, to do the calculation. But anyway, you need to practice. Okay, moving on to question six. Question six, suppose that now we are in the basic probabilities, maybe I should be asked to write in this. Why am I writing POTMAS? Basic probability. Suppose A and B are mutually exclusive.  It's equals to zero. So those are the things that you need to think. Identify effects given in your question. Right? So we do that. Such as the probability of A is equals to set 0.3, which is 30%, and the probability of B is equal to 0.2 or 20%. Which one of the following statement is incorrect? So it means we need to be able to evaluate all the questions. So we can start with question number one. Question number one is a compliment. So they are asking, for you to calculate what is the probability of a compliment of A, which means you need to say 1 minus the probability of A, which is 1 minus 0.30. So this statement is correct, right? Because 1 minus 0.30 is equals to 0.70. Oh, why am I giving you all answers? Oh, me and Bert. Okay. That was the last time that I drew all the answers. I'll just give you the hint. You will need to do the calculations. Number two, the probability of A and B is equals to 0. Is that correct or incorrect? That is correct. That is correct because we already identified it when we were reading the statement. So those two are correct. Number three, the probability of A given B is equals to the probability of B given A. How do I know? I don't know, but we can definitely evaluate that. So the probability of A given B is given by the probability of A and B divided by the probability of B and the probability of B given A is given by the probability of A and B divided by the probability of A. These are straightforward equations of conditional probabilities that you should know. So let's find out if they are both equals to one another. Substitute the values. What is the probability of A and B? It's 0 because we said it right there. Even A and B are mutually exclusive. Divide by what is the probability of B? I'll give you the answer. 0.20 0.20 0.20 And therefore it means it is equals to 0, right? What's about the probability of B given A? It will also be equals to 0 because the probability of A and B is 0. Divide by the probability of A of 0.30 0 divided by another number is the same as 0. So it means they are the same. They are both equals to 0. So they are both equals to one another. So that is correct. We're still looking for the incorrect answer. Probability of A or B. Now it means we need to go and evaluate what is the probability of A or B? It's given by the probability of A. Or B is given by the probability of A. Plus the probability of B minus the probability of A and B. But now since we know that A and B are mutually exclusive. So therefore this will be 0. It means it doesn't exist on the formula. When event A and B are mutually exclusive, the probability of A or B or the probability of A or B will be given by the probability of A plus the probability of B and that is what the addition root states. So is that equals to 0.5? Let's check. Yes. Probability of A is 0.3 plus 0.2. Therefore it's 0.5. That is correct. And if that is correct, then it means we are left with number 5. So number 5 says A and B are independent. How do we know that events are independent? We need to evaluate them. The probability of A given B will be equals to the probability of A. If two events are independent, it means the other event, the given event has no bearing on the probability of an event that you want to calculate. So then it means conditional probabilities, the probability of A given B will be the same as the probability of A. Or you can use the probability of B given A will be the same as the probability of B. So let's check because we need to check either one of them. What is the probability of A given B? The probability of A given B is 0. We did calculate it, we found that it is equals to 0. What is the probability of A? The probability of A is 0. Therefore they are dependent on one another because they are not equal. This is if they are independent. So they are not independent. They are dependent events. And you can also check with the second one if you want. You can use either one. So the incorrect statement is E. Moving on, basic probabilities. I need to go back one step a little bit because if you look at this, question 5, 4, 3, 2, 1. They relate to study unit 1, 2, and 3. You can see that. Study unit 1 doing the introduction of statistics. Study unit 3 plus study unit 2 when we talk about visualization which they mainly if it's part of the visualization. But study unit 3 also touches on the measures, calculating the measures, numerical measures. And study unit 2 and study unit 3. So you can see that they are almost interlinked to one another. So basic probabilities. There are two questions. So question 1, we have dealt with something. I don't know what I put it wrong with. There we go. Question 7, it's also part of the basic probabilities. So you are given the contingency table. What is missing with this contingency table? So the table shows the distribution of 25 students according to gender and preschool experience. And they gave you the event. What is missing here that we will need? Totals. Totals, very important, especially when they gave you events. You need to make sure that you quickly calculate the totals because you will need the totals. Okay, so let's calculate the total. How many are male? 8 plus 6. It's 49 plus 1. 11. 14 plus 11 should be 25. It should be equal to the sample space. 8 plus 9. 17. 6 plus 2. And 8. And 8 plus 17 should give us 25. Okay, so now we've got all what we need. We can be prepared or we are prepared to answer the questions. So it means we need to evaluate each and every statement. So let's look for our incorrect statement. Remember the following. The probability of an event is given by observation satisfying the joint event divided by N. The probability of A and B is given by the joint event. Observation satisfying the joint event divided by the sample space. And our sample space is N. She's always the grand total, right? And we need to always remember the probability of A or B. It's given by the probability of A plus the probability of B minus the probability of A and B. And the probability of A given B is given by the probability of A. And let me not use the end because it looks like I'm writing a sentence and use the sign. A and B divided by the probability of C. So those are the main formulas that you always need to remember. Remember the data that they gave you inside is your joint event. So it's those with an end, the probability of A and B. The outside, like 17, it is your symbol or marginal events, right? And what do we mean by marginal events? Marginal events are addition of two joint events. For example, 17 is made up of joint event, male and preschool and female and preschool. So those are the things that you always need to remember when you answer basic probability questions. So now let's answer this question. What are the events satisfying preschool? What is the probability of preschool? So preschool, it got less of whether they are male or female because it's a simple event. You're going to use the event satisfying the simple event preschool divided by the grand total. I'm doing one and you need to do two. So that will be 17 divided by 25. Does it give us 0.68 during the calculation? Yes, it does. So that is correct. Probability of female, what is the probability of female? 0.44. Are the events satisfying? 11 divided by 25. 11 divided by 25. Does it give us 0.44? Yes. That is correct. So you just said 11 divided by 25 should give us 0.44. 20 event preschool and male. Are the events satisfying male preschool or preschool and male? Events satisfying divided by the sample space. So there are eight divided by 25. Is it equal to 0.32? Yes, ma'am. So that is correct. Number four, we are looking for no preschool of female. How do we define that? The probability of A or B is given by the probability of A plus the probability of B minus the probability of A and B. So therefore we need to do the probability of no preschool plus the probability of female minus the probability of no preschool and female. So what is the probability of no preschool? 8. 8 divided by 25. Probability of female? 11 divided by 25. And divide by 25 minus the joint probability of no preschool and female? 11. No preschool and female? That's two. Divide by 25. So because they all have the same common denominator, you can say the common denominator is 25 and you say 8 plus 11 is 90 minus 2 is 17. 17 divided by 25? 0.68. 0.68, which is not possible. And the probability of preschool given female, if we know the formula says the probability of A given B is given by the probability of A and B divided by B. Therefore we can say the probability of preschool and female divided by the probability of female. And that gives us what is the probability of preschool and female? It's 9 over 25 divided by the probability. Can I ask that we ever play music, please do not switch off the music because that part of the song, if it's copyright song, you won't be able to publish the recording. So it means you would have made everyone who hasn't attended the session miss out on those who want to listen to the recording later on. You won't have, you can't publish with copyright music in. Okay, so the probability of female, so make sure that your music is off. Probability of female, it's 11 over 25. And if we apply math, this is the same as 9 over 25 multiplied by 25 over 11, which is the same as 9 over 11 because 25 and 25 will cancel out. In math, we apply, keep the fraction, the first fraction, change the division to a multiplication and flip your second fraction. What was at the top comes to the bottom, what was at the bottom goes to the top. So your numerator and the denominator, they swap places. And that's what I did. I kept 9 over 25, change the sign to a multiplication and flip my 11 over 25 to 25 over 11 and simplify 25 and 25 cancels out. And we are left with because it would be equals to one and equals to one, nine times one is nine and one times 11 is 11. So what is 9 divided by 11 should be 0,8218. Is that correct? Yes. Yes, ma'am. Hi. And that's how you will answer the probability question, but in the exam when you get to four, you stop right there and move on to the next question. So question eight, you can see that only two questions dealt with basic probabilities. Now we are in discrete probabilities. How do I know that? They gave you the table with x and the probability corresponding to that x observations. A BSE student in statistics applies for five different jobs. Let x represent the number of offers given below are the probabilities of the number of job offers. If they receive zero offer, one offer, two offers, three offers, four offers, five offers, so that BSE student is very clever to receive five offers. Which statement is incorrect with regards to this? And when you get to the discrete probabilities, you always also remember the sign, right? What does it mean? The at most, at least, the less than or equal, the between, inclusive and exclusive and so on. So those are the things that we need to always remember. So let's evaluate the statement. What does at least mean? In terms of a mathematical sign, is it a less than? Is it a less than or equal? Is it a greater than? Is it a greater than or equal or is it an equal? Those are very important to remember. What is at least? It's greater than or equal. It is greater than or equal. So therefore it means it must include two or any of the bigger number. So if we talk about that, it means we need to add all these values. So the probability, the probability of X greater than or equals to two will be the same as the probability of X is equals to two, plus the probability of X is equals to three, plus the probability of X is equals to four, plus the probability of X is equals to five. Or, alternatively, you can say the probability of x is greater than or equals to 2 is the same as 1 minus the probability of x, and I'm going to put it into bracket, x is equals to 0 plus the probability that x is equals to 1, because you just need to do the complement of those four. Instead of adding four numbers in the exam, you can just add the two and subtract them from one. They will give you one and the same thing. So, what is the un-term? 0.786. 0.786, which is not correct, right? Then number two, it says, what is the probability of x less than or equals to 5. So, it means it's all of them. What do we know? If it's the probability of all of them, it's the sum of all probabilities, right? And in terms of basic probabilities, the sum of all probabilities, they are always equals to 1. So, if I have to add all of them from 5 to 0, so it means I expect the probabilities to be equals to 1, because you can also double check it.  I have to add all of them. It is not equals to, and so that will be incorrect. Number three, just going to reduce the font a little bit so we are able to see all the questions. Number three, it says the probability that x lies between two and four with two exclusive and four inclusive. So, what does that mean? That means two exclusive, because it does not have an equal sign. It means we're not going to include two, so it's any number above two, but it also says it should be any number less than or equals to four. So, therefore, it means from four, any number up to there. So, therefore, our answer there should be the probability of x is equals to four, plus the probability that x is equals to three. That's the only probabilities you need. What is that? Remember, we're looking for the correct answer. That is correct. And that is the answer we are looking for. I'm not going to do the expected value and the variance. I'm just going to give you the hints in terms of how you answer those questions, but you will need to go and practice on how to calculate them. So, question four, it says you need the expected value. So, the expected value of a discrete probability is your x observation times its cross-bonding, there should be a sum, is the sum of your x observation times its cross-bonding probability. What does that mean? It means you need to say zero times 0.39, which is x times px, which will give you zero. One times zero comma 175 will be zero comma 175. Two times 0.624 will be 0.648, and like that, until you get to the end and then you do the total. This will be the answer you get when you do the total, ending all of them up. It should give you your expected value as the expected value. How do we then find the next question, which is the standard deviation? The standard deviation, which is sigma, oh, actually it's not the standard deviation, this is the variance. Finding the variance, the variance is the sum of your x observation minus your expected value squared times the cross-bonding probability. What does that mean? It means you're going to say zero minus the answer you get from the expected value, square the answer multiplied by the cross-bonding probability, plus one minus the answer of the expected square, multiply that with the cross-bonding probability, plus two minus the expected value squared, multiply that with until you exhaust all of them and add all of them up, because this summation means aiding up. That will give you your next question. I'm not going to do that. You can practice. Moving on to question. I have a question. So say in the event they don't give us, if you can just move a little bit further yes. So say in the event they don't give us these probability values at the bottom, they gave us actual values, the whole numbers 25, 19 and so on and so on. Would we then have to work out what the probability of each one of those points are before we could go answer those questions or would we get a question like that? Yes, you will have to add all of those frequencies because they would have given you the frequencies and then once you have the frequencies, these probabilities remember is just a proportion. The frequency divided by the total will give you the probability and then you will create your own probabilities in your assignment. In your assignment, you had a question where they tell you they don't give you the probabilities, but they tell you that if they all have the same probability distribution. So it means if there are five, they will have all similar probability distribution, which means one, two, three, four, five, six. So here you have six. So you will just say one divided by six and that will give you your probability. They will all have the same probability of one over six and then you can use that to answer the same question. Okay. Thank you. On to question line. I'm looking at the time and I'm thinking we still have to get to question 25. We are way behind that, but you get the grasp of what is happening. So we are on discrete probabilities. So one question. So discrete probability is one of those study units that you might get three questions because in under discrete probabilities, you have discrete probabilities, the properties of the discrete probabilities. Then you have binomial probabilities and you have Poisson. So you should expect at least three questions from there. So we've dealt with discrete probabilities. Now we're going into Poisson, sorry, binomial. So this is by normal and they will follow the same pattern. So they will not put binomial first before they put discrete probabilities. They will always be like this. So it will be discrete binomial Poisson. So which one of the following statement is incorrect? So it means on this one, you need to know and understand your properties of a binomial distribution. So for the binomial distribution, there are n independent trials. Is that correct? Or are we looking for the incorrect statement? So you must always remember that the outcomes are always independent. So you cannot fail and pass at the same time, right? Because it's failure or success in binomial. There are two outcomes. So it means the trials needs to be independent. So that is correct in terms of the properties of a binomial. Number two, the probability of success, which is the probability of a binomial trial will always be represented by, oh, of success is pi and remains constant. So it cannot be constant. I don't know why they say it's constant. What does that mean constant? What does that mean? But the probability of success is pi. That is correct. The expected value of a binomial is your sample size multiplied by the probability of success, which is correct. The distribution is continuous. That is not correct because it's discrete probabilities. The distribution is discrete. It comes from a discrete process. Remember with numerical values or quantitative data, you have discrete and continuous. Continuous, it's dealt with in normal distribution and sampling distribution. You must always remember that, right? So the incorrect statement here will be number four, because the distribution should be a discrete distribution. There are two possible outcomes. I already touched on this. It's a success or a failure. So that is question right. I'm sorry I answered that question on your behalf, but I was looking at the time before I, yeah, we spend more time trying to figure out what's what. Then we come to another question. It's also binomial. Binomial probabilities as well. Home security has a reliable rate of 45%. In a sample of nine houses, which is n equipped, so this is your pi, equipped with this system experience and attempted backlaries. The probabilities are independent from one home security to the next. Let X represent attempted backlaries. Which one of the following statement is incorrect? So now you need to also use the table. So for those of you who haven't attended any of the sessions that I offer, under the acolyte sessions that we do for statistical literacies, there are nodes. Under those nodes, there are tables. It's written STA 1610 and 1510 statistical tables. Those are the table that you can use and you can also use the same table when you go write the exam. You are allowed to have the statistical table. So the table that I'm talking about looks like this. So you can use that. So you need to go to the binomial distribution table and it is written binomial probabilities if you need to know how to read this table. Very complex, but easy to understand if you practice. So the table has probabilities at the top from 0.01 to 0.5. And at the bottom there are also probabilities at the bottom, but they are on the second page. They also relate to this table. So 0.99. So this one is 0.99 and this is 0.50 at the top and the bottom as well. And the next one is 0.55. So there are probabilities at the bottom and at the top. So how you read the table, the probabilities at the top, you read it with the n values and x values on the left, top with the left bottom. You will read it with the right n and x values. And you can see that your x values at the bottom, they go from below to the top, right? They are in reverse. Whereas on the left, they start from the top, they go to the bottom. So you need to know how to read the table. So going back to our question, our probability of success is 45%, which is 0.45. So on the table, we are going to use 0.45, which is the last column. So since it's at the top, we're going to use n on the side, on the left. They are both on the side. It says a sample of nine homes. So on the table, we're going to look for n of nine in order for us to help to answer this question. So n of nine and at the top. So here at the top, there are probabilities, even though they are missing, you must also remember that there are those ones at the top. So we know that this is 0.50 and 0.45. So the second one should be 0.45. So let's see, second one was 0.45. So then it means we're going to use the last second column. So on nine and we're going to use the last column and our x values are from 0 to 9. We need to validate each statement and find the one that is incorrect. The probability of x is equals to 2. It means exactly 2. 9 x of 2. And you just go to the x. 0.0. Let's make it a little bit bigger. And the answer is 0.1110. 0.1110. So that is correct. The probability that x is equals to 1 equal to 1. It is the second row, which is 0.0339. 0.0339. The probability that x is equals to 0, you go to the first row, 0.0446. 0.0, going back. 0046, 04060. That is the incorrect one. The probability that x is less than or equals to 3, you will just need to go to 3. And let's remove this. Go to 3. And that is 3. And you're going to add all of them. You need to add all of them. 0.046 plus, 0.0046 plus, 0.033. 9 plus, 0.1110 plus, 0.2119. It's 0.3614, which is correct. The standard deviation, you will need to use the formula. It's the square root of your pi. Actually, we must start with n. The sample size times the probability of success times 1 minus the probability of success, which is equals to the square root of 9 times 0.45 times 1 minus 0.45. Square root of 9 times 0.45 times 1 minus 0.45, which is equals to 1.492, which is the same. Good. Are we happy? Are we good? Yes. I just wanted to quickly get the name of the table again. Sorry. This table, it's the binomial table. So in your past exam papers, if you went somewhere online and you downloaded the past exam paper, they are always at the back of the exam paper. You will find these tables in there. Thank you. This is Poisson. Poisson statements will be stated that you are now looking at Poisson. The binomial, they don't always say that it follows a Poisson distribution or something like that. You need to make it up. So this is Poisson, a law enforcement, and you can see that here we have four questions on discrete probabilities. But I guess because this is a trial paper, and probably because it's 2012, it was set by somebody else. But bear in mind that at least some of the questions you might have two or three questions from that study unit. You always get two questions from that unit. So a law enforcement agency claims that the number of times that patrol car passes through a particular neighborhood follows a Poisson process with the mean of three times the night shift. Three times, therefore it means our lambda is equals to three. Let X denote the number of times that the patrol car passes through the neighborhood during a night shift. Which one of the following is incorrect also for binomial? Please use the table. Oh, sorry, for binomial, use the table. What I forgot to mention is that you can also use the formula which is your NCR, which is your combination, times your probability of X times one minus the probability of success and minus X. You can use this formula to calculate the probability of equal. The minute you get to the probability of less than or equal, then it means you will have to use this formula three times. Because if you're doing the probability of X less than three, you will have two. How many did we say? One, two, three, four. You will have to calculate that formula four times to get the answers, all of these answers using the formula. Similar with Poisson, calculate the probability. You can use the formula if you have time. Otherwise, you need to use the table. Because if you calculate the probability of less than two, then it means it's zero, one, and two, three times. You will have to calculate this three times to get the probability of zero, the probability of one, the probability of two, and add them together. Otherwise, you use the table. Easy. Already they have calculated this formula for you. What you need to also remember is your lambda is the same as your mean is the same as your variance, but it's not the same as your standard deviation. The standard deviation is the square root of your average. So if we need to answer the question, which one of the following statement is incorrect? Number one, is it correct or incorrect? Think about time. Is it correct or incorrect? The statement is correct because I just gave you the answer there at the top. Right? I gave you all the answer. This is the variance. What is the probability that x is equals to three? So we need to go to the tables. Go look for Poisson table. And your Poisson is divided by the lambda. So every lambda table has its own set of x value. So you will see that with this table that starts from 0.1 up until one, the x value starts from 0 to 7. You need to pay attention to that because it's very important, especially when you calculate the probabilities of greater than or equal or at least or less or greater than. You need to take that into consideration so that you don't miss out. So we're looking for lambda 3. So it's table 3. And you can see that the x values on table 3 starts from 0 up until 12. It's very important because for 3 you can see that 12 has 0.0001. So you need to pay attention to that. So the probability that x is equals to 3, you just go to the table and the 3x is 3. You just read the value. That is your answer 0.3240. Is it right? Otherwise you can calculate. Yeah, by substituting the value of lambda is 3. So the probability that x is equals to 3, you will say e to the power of minus 3 times 3 to the power of 3, because our average is 3 anyway, divide by 3 factorial. And we will calculate that. But we know that this is correct. The probability that x is equals to 5, you go to 5. It is 0.1008. 0.1008. Let's go double check because the values can be very confusing. You can see that it is incorrect. So that is the incorrect statement and you stop right there and you move on. Okay. And I can see, I think this is the one way they have a typing error. Right? Because if you look at number 5, it says, oh no, there's no typing error because number 5 says the variant. What is the variant? Number 5? The variant is 3. So that is correct.  Let's remove all this. We have to go to x is equals to less than 2. So it means you add all of them. So we will say it is 0.04498 plus 0.1494 plus 0.2240 which is equals to 0.4232 which is correct. So option 3 is the incorrect one. Question 12. Now we are in normal distribution. 50% of the college students attend school within 50 miles of their homes. In a sample of 500 college students, the probability that the sample proportion will be between 0.45 and 0.55. Yes. So this is not normal distribution. This is sampling distribution. So on this trial paper, they didn't follow the normal distribution. So this is sampling distribution. So it's study unit 7. So probably because study unit 7 and study unit 6 are almost linked to one another probably maybe hence they are also interchangeable like this. So we're dealing with sampling distribution of the proportion. So they told you that 50% of their students, so it means our probability of success or whatever we call it, the population probability. In a sample of 500 which is our n and our p small p is given by that. So we need to find the probability that small p is between 0.45 and 0.55. So it means we're going to have to standardize this by using p minus the proportion divided by the standard error which is the population proportion 1 minus the population proportion divided by n.  So we need to find the probability of 0.45 minus our population proportion is 50% which is 0.5 divided by the square root. Hey, why is my thing doing zigzag? Like now I've got arthritis. Hey, okay, maybe it's the pen, it's not me. 0.5 times 1 minus 0.5 divided by 500. 0.55 minus 0.5 divided by the square root of 0.5 times 1 minus 0.5 divided by 0.5. p will be equals to, we just need to calculate the values. Have you calculated the values? Let's see 0.45 minus 0.5 divided by the square root. I'm using a casual calculator, so let me not say the words the way I'm seeing it because I'm just doing my fraction calculator calculations. So if you are not using a casual, you will have to do things step by step. So on the 0.45 is minus, I need to keep only 2 decimal, 2.24 because the answer is minus 2.3606, but I need 2 decimal and you will see why we need 2 decimal. And on the other, I shouldn't have removed everything, 0.55 minus 0.5 divided by the square root of the fraction, just 0.5 and the answer this side is positive 2.23, 2.4, 2 decimals, 2.4. Okay, so now what you also need to remember when we deal with probabilities are the following. When we go to the table, the probability that z lies less than a value, the value we find on the table will be that probability that we are looking for. If it's the probability of z greater than a value, when we go to the table we need to say 1 minus the value we see on the table. If it is between, if z lies between two values a and b, we're going to say the table value for b minus the table value for a. So we're going to apply the same rule, right? The same rule that I'm applying here on this question because it is between. So this is our a and this is our b. So we need to go to the positive side on the table. So we go to the cumulative standardized normal distribution table. She's the first table and we're going to go to the positive side. It has the cumulative standardized normal distribution has two sides, the negative side and the positive side. So we're going to go first to the positive side and we'll find 2.24, 2.2 and then 4 at the top. So 2.24, we find 2.2 on the left and the last digit, we always find it at the top. So where they both meet, that is the probability we're looking for, which is 0.9875. So that will be 0.9875 minus and we go to the negative side and minus 2.24. On the negative side, we do the same. We will find negative 2.2 and 4 at the top where they both meet. That will be the probability we're looking for, which is 0.0125. Which is 0 comma 0125 and we just subtract 1 from the other. 0.9875 minus 0125, 0,0,0,1,2,5. And the answer is 0 comma 9750, which is option 4. That's how you will find the probabilities. Now with the next question, where is question dating, where they give you statements and the values, therefore it means you need to evaluate each one of them.  So number one, you're going to find the value on the table under minus 1.44 and subtract that from 1. So let's go and do that. Minus 1.44, so we'll find minus 1.4 on the side and 4 at the top and we're going to take this value and subtract from 1. 1 minus 0.0749 and that should give us the answer that we're looking for, which is correct. And you can stop right there and move on to the next. You will need to go and validate the rest of the values. So z of less than 2, I'm not going to do the rest of them. Z of less than 2, you just go to the table because the side says less than, that will be the table value, less than the table value, greater than 1 minus the table value. So you'll go and find 1.59 and the value you see on that table, you subtract it from 1. This one, you will use the table value to validate. Okay, moving on to question 14. I'm aware that we left it 12 minutes and I think if we can get to question 15, 16 because the other question is not long ago that we dealt with those chapters, like study unit 10, 11 and 12, you have dealt, study unit 11 and study unit 10. You did that recently, so it's not going to be a problem. Okay, so those were, I'm going to say this is also normal distribution, but it can also be sampling distributions. So at least there are two questions from there. Okay, it is important for an airline to know the appropriate total weight of the baggage carried on each plane. An airline researcher believes that the mean baggage weight for each adult is 60 kg. To test his belief, now we're testing beliefs, so we are in hypothesis testing. This trial paper does not follow the structure of your study unit, so I've already made that connection because now after doing sampling distribution and doing the sampling distribution and doing the normal distribution, you should be moving into confidence interval, but let me not state that this is a hypothesis because I need to read the entire question. It might not be hypothesis testing, it might be still normal distribution. To test his belief, he draws a random sample of 50 adult passengers and weigh their baggage. He finds the sample mean to be 57.1 kg. If he knows that the population standard deviation is 10 kg, the probability that the average baggage is more than 55, so it means we need to calculate the probability that the sample mean is greater than 57.1. So based on that, because we have the sample size n, so we're still in the sampling distribution. We're still in the sampling distribution, so therefore it means we need to calculate or standardize the greater than sample mean minus population mean divided by the standard error, which is the population standard deviation divided by the square root of n. And since they gave us the population standardization, so it makes everything easy. So calculate the probability of z greater than our sample mean is 57.1. Our population mean is 60 because that's what they gave you there. This is your x bar. Divide that by your population standard deviation of 10, which is sigma. Divide by the square root of 50. And the probability that the z is greater than and we just do the calculation. 57.1 minus 60. The answer is minus 2.05 minus 2.05. So because it is the probability of a greater that, so to find the probability of the mean greater than 51.7 or 57.1 is the same as 1 minus the probability of z less than minus 2.05. So it means I must go to the table to find minus 2.05. So minus 2.05 be 0.0202. 0.0202, which then is equal to let me double check the values at the top should be 5, right? And minus 2.0. So I did 1 minus 0.0202 is equal to 0.9798, which is option 1. Option 15. We are in hypothesis testing because I can see that we're doing hypothesis testing. So in testing the hypothesis, so you need to know the six steps of hypothesis testing. So but anyway, the null hypothesis states that the proportion is or the population proportion is 0.40 and the alternative is greater than 0.40. So I'm doing a one-tail test. This is a one-tail upper, upper test. And at alpha or level of significance of 5%, which is the alpha value of 0.05, if the sample proportion is 0.5 and the sample size is 49 and the standard deviation for the proportion is standard deviation for the proportion, it means you need to calculate the standard error. Standard deviation for the proportion is the population proportion divided by the square root of n. So our, oh, I'm talking about proportions, right? No sample mean. Let's go back. My bad. Sample proportion and here they gave you only the the sample proportion. So we're going to use the square root of your population or your sample proportion one minus sample proportion divided by n. So the square root of 0.45 times one minus 0.45 divided by our sample size of 49 and that will be, that is equals to 0.0711. Probably because they would have calculated this regularly as well. I'm going to assume that question 15 they would have said is number two. Let's see. Let's double check the access question. Sorry, my bad. I see where I went wrong. They did give us the population proportion. I used the sample proportion instead of the population proportion. So this will be your population proportion comes to your popular because they gave us the hypothesis testing where the population proportion is given. I'm thinking of your assignment where the population proportion was not given. So you needed to use the sample proportion. So that we delete the five zeros everywhere and seven zero. It would be 0.06999985 which is option two. Okay. And using the same statement, consider the following information on question 15 what will be the critical value. So remember now the critical value and pay attention to detail. We're doing a one tail, upper tail, one tail test. So therefore our critical value is z alpha. If we were doing a two tail, we will divide by two. So we're doing a one tail. So it will be z of 0.05. So it means we need to go to the z table inside the z table. Yeah, on the right place. Look for inside the table. Going to look for 0.05. 0.04905 will be one of those two values. And therefore it is an exceptional one, which the critical value will be one minus one point or because it's in the upper tail, it will be positive. 1.645. It's 1.645. And because it is in the upper tail, because it's greater than that, so it will be in the positive. 1.645. Your mean is at that point. Option two will be the correct answer. You need to pay attention to the information given. So if the sign here was a two tail, then you will have two regions of rejection. Your critical values, there will be two of them. But if you would have divided your alpha by two, if it was in the less than or the lower side, you would put it on the less than side and it would be negative. Pay that close attention to that. So our type actually is up. I will post this where the notes sections are, but at least this gives you some ideas in terms of how the questions are. They look almost exactly the same as what you did in your assignment.  Okay, so before you leave, I just want to also share in their chat where you will find multiple desktop open. I need to navigate to my desktop so I can get the things I want to give to you. This is going to be one. Just want to share in the chat. For those of you who don't know where to find, actually I don't want to share the, because I want to share the recording. The recording. Okay, in the chat, I'm sharing the link to the way you will find the recording. But on that note as well, I want to go there so I can share my screen. I'm sharing it up there so that we can talk about that as well. So on the link that I shared with you, if it's for the first time seeing what I'm showing you, probably you should get excited because this is where you will find the recordings for all the sessions that the Western Cape Paro offices offers. So we've got tutorial classes. If you do any of the modules that are here, you can go and watch the recordings. If you do in the writing center, that's where the other colleagues in terms of academic literacies in the writing center for the English and other facilitation that they do, you can find also the recordings. So if you do English, you will find tutorial classes as well as the Akalit classes. So there will be two, so you can watch both of the recordings because they do different things. Tutorials are different from Akalit. And I'm in the numeracy center. So in our site, you will go to a basic statistical literacies, which is the session that we are on. If you click on that link and you will see that since from April, we had several sessions. All the recordings are uploaded. It takes time to reflect on the other recordings. So you will see today's recording as well. It will appear here next week or even during this week. So you should be able to see all the recordings for the previous sessions. I don't know why this recording is not working. I will ask them to check that. But all the sessions, you can see that we do have all of them. So when I was explaining, if you don't know how to use your calculator, this session, we are using a casual calculator, financial math calculator, and the sharp scientific calculator. You can come to this on the 29th of April to see how we answer those sessions. But those are the links I wanted to show you if you go up again. So on the same link, when we click on open class notes, you will find all the notes for all the sessions that we had. And I'm going to post inside here as well. So the ease, the tables, we are the tables. I know that I did post them. So here are the table. So you will find the table. You will also find a document on functions to use to calculate the mean, the standard deviation and all that. You can follow the document as well. It explains all different calculators, the casual calculator and the sharp calculator. You can find the information there. We do have also some templates that we used for study unit 10 and study unit 11. You can also use them if you watch the recordings on those sessions. You can also follow that by downloading this do not open this template here. You need to download them and use them on your machine so that you don't save and change and make changes to them. And I'm going to post here the file paper that I just used to upload it. So you will find this. So you will find it here. There is no need for me to send it to anybody. You can come here and download it. You saw that there are questions and then there are solutions at the end. What I would suggest you do is work through the trial paper. And once you are done, then go and look at the responses to see if you are doing right. Because that's how you will practice and know where you are going. And it is a detailed trial paper. It's got all the solutions and step by step on how you answer every option of the solutions. Of the questions as well. So those are the things I can share with you right now. I want to wish you all the best of luck with your exams. Remember if you need to ask any questions relating to STA 1610 content, you can send an email. I forgot. I need to also tell you, by email, actually, it is on the document. So I don't even have to tell you how to get there. So there is my email on every documentation that is uploaded, almost all the documentation. My email address is there. So you can send an email, but you need to copy CT and type it, unisa.ac.za, when you send that email. Otherwise, those who are on the WhatsApp group, we can always continue to chat, even though the WhatsApp group is muted, nobody talks, but you do have that opportunity as well. And on that note, it completes today's session and it completes 2022 sessions. I want to wish you all the best with your exams. Those who already have started writing exams, good luck with your results and those who are still going to write all the best. And goodbye, unless if there are any questions or comments. None at the moment. But thank you so much. If there are absence of questions and comments, goodbye. I will see you at the corridors of South Africa. And all the best. Bye. Thanks, Lizzie. Thank you.


Optional Equipment for CNC Milling Machines In this video, we will tell you about optional equipment for CNC milling machines and find out how they work and what they are used for when machining material. This is Watson. Welcome to the world of CNC machines. Vacuum Table The vacuum table presses the workpiece onto the working area of the machine through special holes. Design Presses the workpiece over the entire area, preventing it from shifting and subsequent rejects. Leaves no splits or cracks, unlike clamps. Fast and easy clamps the material to the work table. Aspiration System The aspiration system is an industrial stationary dust extractor with a corrugator and brush that are attached to the spindle. The system sucks chips and dust into a special bag during operation. Advanced aspiration systems not only clean the workplace but also filter the air. DSP Controller The DSP controller is a remote controller connected to the machine. While the machine is running, you can adjust program parameters, increase or decrease spindle speed, set the zero point, stop the program, run the layout from a USB stick. With it, there is no need for a separate computer to control your CNC router. Coolant System Coolant system is used when working on metals to prevent overheating of the tool and material. A specific liquid, such as water, oil or emulsion, is supplied to the milling point through a nozzle. It is then driven back through a groove along the machine housing to a pump where it is filtered and fed back into the working area. Rotary Device The rotary device allows the milling and engraving of cylindrical workpieces, expanding the capabilities of the machine. The milling machine becomes a versatile automation unit with the advantages of a lathe. The rotary device makes it possible to produce furniture legs, columns, balusters, chest pieces, souvenirs. Automatic Tool Change All tool changes are automatic with no operator intervention. All you need to do when using an automatic tool change system is to select the tool according to the machining program, install it in the tool nests, set the settings and start the program. Tool Height Sensor Button The tool height sensor is used to detect tool height in the Z-axis. It operates by closing the contact when the tool touches the metal plate of the sensor. It facilitates tool changes and is easy to use. The sensor is resistant to mechanical stress, chips and coolant. Gantry Leveling System The system automatically aligns the gantry along the Y-axis. If the gantry is not aligned, it is not perpendicular, which can lead to jamming of one of the drives and skipping steps. We have told you about eight options to make working on milling machines easier and simpler. If you still have questions, feel free to contact our engineers. Write in the comments what else you would like to know about milling machines. Give us a like if the video was useful. This is Watson. See you in the next videos.


And we also appreciate very much the cooperation you've given us with the Middle East peace initiative. It was my pleasure today to have an extensive discussion with President Torn and other representatives of the European Commission. Our discussions focused on the Williamsburg Summit, as you can imagine. This will bring President Torn back to the United States next month. President Torn demonstrated his support for close and friendly relations between Europe and the United States during years of distinguished service as Prime Minister and Foreign Minister of Luxembourg. Our discussions today have demonstrated that his dedication to these objectives is just as vigorous in his present role as President of the European Commission. Our discussions on summit preparations have strengthened my conviction that the meeting at Williamsburg will be a valuable opportunity for a free and open exchange of views on the problems and opportunities the world presents to us. It's especially an opportunity to help to create a basis for sustainable, non-inflationary growth in the world economy and to strengthen the international trading and financial systems and the links between them. The European community, our largest overseas trading partner, will be essential to that effort. We agreed also that the United States government and the commission must make urgent efforts to find solutions to the differences we have on international trade issues. We're both committed to avoiding any slide into protectionism. We also noted with satisfaction the progress made in various organizations toward a common Western approach on questions of East-West economic relations. President Torn, welcome, and it's good to have you back. Thank you, Mr. President. Thank you. Ladies and gentlemen, I have nothing to add to what the President said. I'm in full agreement with him, but we had a good meeting and I'm now even more confident than when I came that Williamsburg will be a success and will cooperate in order to make it a success. Thank you.


Hell yeah, guys. What's up? This is Chris Pike. My friends call me Banksy. I'm back again guys and today we got a special topic It's a topic. I want to talk about it's a big deal right now a lot of the gamers gameplay community and the developers are weighing in on this and in particular drumroll day one game reviews first off What are your opinion about day one game reviews because here's the thing the faster a website gets a review Out the more search engine results. They're gonna get in general This is an overstatement and this is a generalization I get that but if you're the first one out with a review you get the lion's share of the clicks at least up front from From Google so here's the problem these sites that are producing Reviews within an hour or two of a release They're not really that good of reviews in theory because they haven't had a chance to play the game Let's take for example. I don't know destiny You know what they got lots and lots of hundreds of hours of content although in the the websites defense the first four hours are Pretty cool, but the rest you know a lot of people are saying it's kind of just doing the same thing over and over again But no joking aside think about a game like World of Warcraft Whatever that is the new expansion the Draenor. I'm an orc I built a garrison and I grew a beard and I threw away my social life and Whatever it's called Warlords of Draenor. That's the one guys that game comes out that game's got like I don't know three or four weeks of content in theory, right? If you're a casual gamer it's gonna take you a few weeks to get through all the new stuff all the new zones Try out the new equipment get used to all the new systems Yada yada yada you get my point But here's the thing a game site releases a review in three hours Google because it can't fact check it doesn't have the ability to fact check or you know check the validity of these Reviews really like they could check up a website's legit, but they can't go through an individual review They will actually in theory send signals out saying hey, there's a new review It goes up it gets search engine priority and these sites are now getting views They're getting views giving out reviews and these reviews impact people's decisions to buy games And they haven't had a chance to actually play the game now there are notable exceptions for example if a if Game site for example is given a game in advance So they can actually play through the whole damn thing or at least a large portion of it and give a fair and reason review That's one thing but when you got a you know kind of fly-by-night site that doesn't have that sort of access or an Upstart site maybe you have one and this is totally legit, but you can't get the review you can't get the game right away you post a review or somebody else posts a review post their opinion and Bang, you know what you can actually sink or swim a site or a game based on that alone Pardon me So what's your opinion on day one game reviews in that type of circumstance? Also our developers should they be given like a few day leeway so that you know They're when they release the game if it comes with bugs and it's got some issues You know sometimes where the servers aren't entirely tweak You know what you give it a couple days and all of a sudden that stuff is figured out no problem Let's take World of Warcraft for example and we'll contrast that to like Drive Club or whatever hell that was for PlayStation 4 World of Warcraft when it released a new patch released or the new Not new patch near The new expansion released that game came out right quick They had a whole bunch of issues in the first 48 hours. They had issues, but we knew it would have issues They've got hundreds of servers with millions of players. They got a lot of balls to juggle And Anyways guys, do you give them a pass should a review that comes out in the first day that says this game's terrible I can't connect blah blah blah, which is which is a real complaint. Should that be given a review? Should that be included into Metacritic? Maybe I don't know That's one of my arguments the other one is and I'm still trying to think about it is Drive Club That game is a lot different World of Warcraft sorted their stuff out generally within like 48 to 96 hours And five free days of gameplay were given out so that so they remediated but Drive Club for the PlayStation 4 has been a gong show It's been out like almost four weeks now I think and they still don't have it together their servers are down.  They shouldn't be given a pass But where do you draw the line guys? What do you do? Anyways, that's enough of a rant for this because we're gonna talk about this topic again But please weigh in on your opinions. What websites do you go to a couple websites that you trust?  It's actually gonna play the game not just try and steal Steal a search engine optimization and search use and search hits because of you know releasing a game review early What do you guys think weigh on this guy says your boy big see I'm gonna be back and I'm gonna be taking on this topic again This is check it out


Do you love Joey? Yeah. Why? Because he's tasty? Yeah. Joey's tasty? Yeah. Baby shark. Baby shark. Tommy shark. Tommy shark. No more sharks. No. Bella, who's baby shark? Do you know how to open presents? I think I wrapped it up pretty good too. Like what? Like as if she... I made it extra hard for her. Bella, this is for you. Alright, ready? Go ahead. It's not a house of wrapping, so look. George got me this today because I love classic Mario. But Adam's excited and George said he had to wrap it for me and like give it to me. I'm like, nah, I have to hook it up. I'm gonna go monitor. Yeah, I want it. I need like a 50 foot HDMI cable. You know why? To get from the projector to its like house. Does it make a smaller picture? Because it's smaller in... No. Now I realize that's not a smart question. Make like a hand house. The old one was way bigger than this. Maybe just because we were smaller? Oh, so smaller console, smaller picture. Mommy's gonna get her tea. Let's go get mommy's tea. Oh, yeah. That was good. Official play, what if I never play again? Guys, this is not a sponsor. I just love Nintendo. Yeah, just a little computer. We can take it to vacations.  Yes. Oh my God, it has English, French and Dutch. And Portuguese and Portuguese. Portuguese. Wow, this is big size.  It says everything's in each other's heart. That's the lighting I've been looking for. No, no, no, right there.  And my books. I'm obsessed with books guys. I read like crazy and I paint weird abstract stuff and I like cards. I have collections and collections. Here's the deal. I bought Bella for her birthday because I'm all about education and reading. I believe in reading and dreaming. That's my other motto. Hashtag reading and dreaming. So I got Bella a whole bunch of books, like lots and lots of books. They're used books because I wanted to get a lot of them. They're recycled, someone else learned from them and then they go to a new home and new love and they keep living. Exactly. I want to show you all the books because I have picked every single one of them. Look how many books I got her. Oh my gosh. So cool. Right? So I got, I really picked out a variety of like books for now. I know what she's laughing at this because I'm very big on etiquettes. Dance at grandpa's. Yeah, because you like dancing. Yeah, it's so cute. Birds. Oh, some of the books are mine. The world. There might be a few parrot books in here. Oh, H is for love. Oh, I'm sure Amazon Parrots is yours. Yeah. Cockatiels. You would have one of my daughters. A bird expert. Benji on the barking bird. Benji! Is that Benji, Benji? Benji, the dog Benji. The chameleon handbook is also mine. Bambi's surprise. Love bird. Oh yeah, birds of North America. My sandy spiders. Oh my gosh, it's amazing. Yeah. This is her birthday present. She's a dog. Book. You say. Which one did she pull out? Little monster. Yes, she pulled out the manner book. This is going so well. She's like looking through. She's got the animal. She loves books. And there she goes. She's going to sit down. Up. She said up. She said up. I'm so proud. Say bye, Jenna. Bye, Joey. Are you upset she left? Are you upset? Ella loved the present. The books I gave her. Oh my God, she loved them. She said books. She said books. You brought Elmo and she still wanted the books. That's my girl. So happy I love it. Let's play Nintendo now. I heard you were playing with Bella. And I missed it. Are you looking for her? He's looking for her. Oh baby. Weirded out by the camera. Vinny, Vinny, Vinny, Vinny. What are you doing? I'm getting Nellie. Ready for bed right now. Vinny. Oh you know. What are you doing with all this stuff? It's cap in the world. What? Monty's helping me take my makeup off, right Monty? Are you sweet? Okay guys, thank you for watching this episode, Monty. Let me know in the comments which bird is your favorite to watch in my videos. Not just that and Nellie and Monty, but out of all of them. I think I got them all in today. I hope I did. Sometimes it's like a losing count. Okay, I'm fading. You can totally tell. I love you guys so much. Bye. Guys, guess what? This thing is playing upstairs? Because I guess whatever is on the TV downstairs is on the TV upstairs. Oh hi. That is all. It took me two hours to get the birds ready for bed. So I haven't even gotten to play yet. Monty, are you ready for bed?