When all possible simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size, n.

Question

When all possible simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means  will be normal, regardless of sample size, n.

Quizplus · Accepted Answer

This is a property of the central limit theorem, which applies to normally distributed populations. As long as the sample size is sufficiently large (roughly n > 30), the distribution of the sample means will be approximately normal, even if the population itself is not normally distributed.

When All Possible Simple Random Samples of Size N Are