Statistical Inference: A Short Course

Appendix 6.A The Normal Approximation to Binomial Probabilities

As we shall now see, normal probabilities can serve as useful approximations to binomial probabilities. This is because, as increases without bound, the normal distribution is the limiting from of the binomial distribution provided , the probability of a success, is not too close to either 0 or 1. So if is a binomial random variable with mean and , then, for integers,

(6.A.1)

This normal approximation works well provided

To improve the approximation provided by Equation (6.A.1), let us introduce the so-called continuity correction (which is needed because we are using a continuous distribution to approximate a discrete one). ...