As a general rule, the normal distribution provides a good approximation to 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 greater than 0.50
D) the underlying population has a small standard deviation and n is large
E) np and n(1-p) are both greater than 5

Question

As a general rule, the normal distribution provides a good approximation to 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 greater than 0.50
D) the underlying population has a small standard deviation and n is large
E) np and n(1-p) are both greater than 5

Connor Detiveaux · Accepted Answer

Final Answer : E, Explanation :  The normal distribution is a good approximation to the sampling distribution of the sample proportion only if both np and n(1-p) are greater than 5. This condition ensures that the sample proportion distribution is approximately symmetric and bell-shaped, which makes it suitable for using the normal distribution to calculate probabilities and construct confidence intervals. The other criteria (sample size, population proportion, and population standard deviation) are important but not sufficient by themselves to guarantee the validity of the normal approximation.

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