If is the mean of a simple random sample taken from a large population and if the N population values are normally distributed, the sampling distribution of is also normally distributed, regardless of sample size, n.

Question

If  is the mean of a simple random sample taken from a large population and if the N population values are normally distributed, the sampling distribution of  is also normally distributed, regardless of sample size, n.

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normal regardless of the population distribution, as long as the sample size is large enough (typically n > 30) or the population distribution is normal. Therefore, the statement is true.

If Is the Mean of a Simple Random Sample