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

This statement is true. The central limit theorem states that regardless of the distribution of the population, the sampling distribution of the mean will be approximately normal as the sample size increases, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size. Therefore, if the population is normally distributed, the sampling distribution of the mean will also be normally distributed regardless of sample size.

If Is the Mean of a Simple Random Sample