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If mean = 0, standard_dev = 1, and cumulative = TRUE, NORMDIST returns the standard normal distribution, NORMSDIST. The equation for the normal density function (cumulative = FALSE) is: When cumulative = TRUE, the formula is the integral from negative infinity to x of the given formula. NORMDIST(x,mean,standard_dev,cumulative). The NORMDIST function syntax has the following arguments: X Required. The value for which you want the distribution. Mean Required. The arithmetic mean of the distribution. Standard_dev Required. The standard deviation of the distribution. Cumulative Required. If and, the distribution is called the standard normal distribution or the unit normal distribution denoted by and a random variable with that distribution is a standard normal deviate. In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. A standard normal distribution table shows a cumulative probability associated with a particular z-score. Table rows show the whole number and tenths place of the z-score. Table columns show the hundredths place. The cumulative probability (often from minus infinity to the z-score) appears in the cell of the table.  How to Use This Table. The table below contains the area under the standard normal curve from 0 to z. This can be used to compute the cumulative distribution function values for the standard normal distribution. where a is the value of interest. This is demonstrated in the graph below for a = 0.5. The shaded area of the curve represents the probability that x is between 0 and a The Standard Normal Distribution. The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation. For the standard normal distribution, 68% of the observations lie within 1 standard deviation of the mean; 95% lie within two standard deviation of the mean; and 99.9% lie within 3 standard deviations of the mean. To this point, we have been using X to denote the variable of interest (e.g., X=BMI, X=height, X=weight). Standard Normal Distribution Table. This is the bell-shaped curve of the Standard Normal Distribution. It is a Normal Distribution with mean 0 and standard deviation 1. It shows you the percent of population: 1  between 0 and Z (option 0 to Z). 2  less than Z (option Up to Z). 3  greater than Z (option Z onwards) Cumulative Distribution Function. The formula for the cumulative distribution function of the standard normal distribution is. \(F(x) = \int_{-\infty}^{x} \frac{e^{-x^{2}/2}} {\sqrt{2\pi}} \). Note that this integral does not exist in a simple closed formula. It is computed numerically. The equation for the standard normal distribution is. \(f(x) = \frac{e^{-x^{2}/2}} {\sqrt{2\pi}} \). Since the general form of probability functions can be expressed in terms of the standard distribution, all subsequent formulas in this section are given for the standard form of the function. The simplest case of a normal distribution is known as the standard normal distribution. This is a special case where μ=0 and σ=1, and it is described by this probability density function : The factor in this expression ensures that the total area under the curve is equal to one. In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.
https://support.office.com/en-us/article/NORMDIST-function-126DB625-C53E-4591-9A22-C9FF422D6D58 https://en.wikipedia.org/wiki/Normal_distribution http://stattrek.com/probability-distributions/standard-normal.aspx http://itl.nist.gov/div898/handbook/eda/section3/eda3671.htm http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_Probability/BS704_Probability9.html http://www.mathsisfun.com/data/standard-normal-distribution-table.html http://itl.nist.gov/div898/handbook/eda/section3/eda3661.htm https://en.wikipedia.org/wiki/Normal_distribution
what is cumulative standard normal distribution