As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if:
A) the sample size n is greater than 30
B) the sample size n is greater than 100
C) the population proportion p is close to 0.50
D) the underlying population is normal
E) np and n(1 - p) are both greater than or equal to 5

Question

Quizplus · Accepted Answer

The best choice is E because it is the correct condition for using the normal distribution to approximate the sampling distribution of the sample proportion. If np and n(1-p) are both greater than or equal to 5, then the sample size is large enough to assume that the sampling distribution is approximately normal regardless of the underlying population distribution. This condition ensures that there are enough successes and failures in the sample to justify the normal approximation.

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