If the sampling distribution of the sample means approximates a normal distribution,then the population must be normally distributed.

Question

Quizplus · Accepted Answer

While a normal distribution of the population may result in a normal distribution of sample means, it is not a requirement. The Central Limit Theorem states that as sample size increases, the sampling distribution of sample means will approach a normal distribution regardless of the shape of the population distribution. Therefore, a non-normal population can still have a sampling distribution of sample means that is approximately normal.

If the Sampling Distribution of the Sample Means Approximates a Normal