If all possible samples of size n are drawn from a normal population, the probability distribution of the sample mean is an normal distribution.

Question

If all possible samples of size n are drawn from a normal population, the probability distribution of the sample mean  is an normal distribution.

Quizplus · Accepted Answer

This is a well-known property of the sample mean for normal populations, known as the Central Limit Theorem. As the sample size increases, the distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

If All Possible Samples of Size N Are Drawn from a Normal