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) $n p \geq 5 \text { and } n ( 1 - p ) \geq 5$
B) $n p \leq 5 \text { and } n ( 1 - p ) \leq 5 \text {. }$
C) $n p \geq 5 \text { and } n ( 1 - p ) \leq 5$
D) $n p \leq 5 \text { and } n ( 1 - p ) \geq 5$

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) $n p \geq 5 \text { and } n ( 1 - p ) \geq 5$
B) $n p \leq 5 \text { and } n ( 1 - p ) \leq 5 \text {. }$
C) $n p \geq 5 \text { and } n ( 1 - p ) \leq 5$
D) $n p \leq 5 \text { and } n ( 1 - p ) \geq 5$

Quizplus · Accepted Answer

The normal approximation to the binomial distribution is considered adequate if both $np \geq 5$ and $n(1-p) \geq 5$, ensuring that there are enough expected successes and failures.

Given a Binomial Distribution with N Trials and Probability P np≥5 and n(1−p)≥5n p \geq 5 \text { and } n ( 1 - p ) \geq 5np≥5 and n(1−p)≥5

Given a Binomial Distribution with N Trials and Probability P $n p \geq 5 \text { and } n ( 1 - p ) \geq 5$