Using the central limit theorem, applied to the sampling distribution of the sample proportion, what conditions must be met?
A) np ≥ 5 and n(1 - p) ≤ 5
B) np ≤ 5 and n(1 - p) ≥ 5
C) np ≥ 5 and n(1 - p) ≥ 5
D) np ≤ 5 and n(1 - p) ≤ 5

Question

Quizplus · Accepted Answer

The central limit theorem applies to the sampling distribution of the sample proportion when np and n(1-p) are both greater than or equal to 5. This ensures that the sampling distribution is approximately normal. Therefore, the correct conditions are np ≥ 5 and n(1 - p) ≥ 5, which is choice C.

Using the Central Limit Theorem, Applied to the Sampling Distribution