Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if:
A) $n p \geq 5$ and $n ( 1 - p ) \geq 5$.
B) $n p \leq 5$ and $n ( 1 - p ) \leq 5$.
C) $n p \geq 5$ and $n ( 1 - p ) \leq 5$.
D) $n p \leq 5$ and $n ( 1 - p ) \geq 5$.

Question

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if: 
A) $n p \geq 5$ and $n ( 1 - p ) \geq 5$.
B) $n p \leq 5$ and $n ( 1 - p ) \leq 5$.
C) $n p \geq 5$ and $n ( 1 - p ) \leq 5$.
D) $n p \leq 5$ and $n ( 1 - p ) \geq 5$.

Quizplus · Accepted Answer

The conventional rule of thumb for the normal approximation of the binomial distribution is that both $n p \geq 5$ and $n ( 1 - p ) \geq 5$ must hold. This ensures that both the mean and variance of the binomial distribution are sufficiently large for the normal approximation to be accurate.

Given a Binomial Distribution with N Trials and Probability P np≥5n p \geq 5np≥5

Given a Binomial Distribution with N Trials and Probability P $n p \geq 5$