As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both $n \hat p$ and $n \hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).

Question

Quizplus · Accepted Answer

The rule that both $n\hat{p}$ and $n\hat{q}$ must be at least five for the normal approximation to be used is a guideline to ensure that the sampling distribution of the sample proportion is sufficiently close to a normal distribution for the approximation to be reasonable. This is based on the central limit theorem and the properties of binomial distributions.

As a General Rule, the Normal Distribution Is Used to Approximate