As a general rule, one can use the normal distribution to approximate a binomial distribution whenever nπ and n(π - 1) are at least 5.

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Quizplus · Accepted Answer

This is a well-known rule of thumb for approximating a binomial distribution with a normal distribution. It is based on the fact that the binomial distribution becomes more bell-shaped as n increases, so it can be approximated by a normal distribution with a mean of μ = np and a standard deviation of σ = sqrt(np(1-p)). However, this approximation is only valid if certain conditions are met, such as n being large enough and p not being too close to 0 or 1. The rule nπ ≥ 5 and n(1-π) ≥ 5 is often used as a guideline for determining when the normal approximation is appropriate.

As a General Rule, One Can Use the Normal Distribution