Biology 2244A/B Lecture Notes - Lecture 9: Central Limit Theorem, Penicillin, Simple Random Sample
23 Apr 2016
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As the number of observations n gets larger, the binomial distribution gets close to a normal distribution. When n is large, we can use normal probability calculations to approximate binomial probabilities. Suppose that a count x has the binomial distribution with n observations and success probability p. when n is large, the distribution of x is approximately normal, The accuracy of the normal approximation improves as the sample size n increases. It is most accurate for any fixed n when p is close to 0. 5 and least accurate when p is near 0 or 1. Binomial distributions become more skewed as p moves away from 0. 5. Based on the above, as a rule of thumb, we will use the normal approximation when n is so large that np 15 and n(1 p) 15. For slightly more accurate results with the normal approximation, you can use a continuity correction.
