Question

Normal distribution could be used to approximate the binomial distribution under certain conditions. We already know the binomial probability distribution formula, so why is it necessary to learn this one? When is it useful to approximate the binomial distribution as normal? Provide an example.

Answer 1

Normal distribution could be used to approximate the binomial distribution n is large and/or p is close to ½, then X is approximately N(np, npq).

Sometimes, due to the factorials in the formula, it is difficult to compute binomial coefficients. The normal approximation allows us to bypass any of these problems by using standard normal approximations.

Sample Question:

Sixty two percent of 12th graders attend school in a particular urban school district. If a sample of 500 12th grade children are selected, find the probability that at least 290 are actually enrolled in school