Continuity correction factor

Because the normal distribution can take all real numbers (is continuous) but the binomial distribution can only take integer values (is discrete), a normal approximation to the binomial should identify the binonial event "8" with the normal interval "(7.5, 8.5)" (and similarly for other integer values). The figure below shows that for P(X > 7) we want the magenta region which starts at 7.5.

Superposition of binomial and
normal distributions
Example: If n=20 and p=.25, what is the probability that X is greater than or equal to 8? Hence for small n, the continuity correction factor gives a much better answer.

Competencies: Use the normal approximation with the continuity correction factor to approximate the probability of more than 40 successes if n=60 and p=.75.

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