If random samples of size n = 36 are drawn from a nonnormal population with finite mean and standard deviation , then the sampling distribution of the sample mean is approximately normally distributed with mean and standard deviation

Question

If random samples of size n = 36 are drawn from a nonnormal population with finite mean  and standard deviation  , then the sampling distribution of the sample mean  is approximately normally distributed with mean  and standard deviation

Quizplus · Accepted Answer

This is the central limit theorem, which states that regardless of the distribution of the population, as long as the sample size is sufficiently large (n > 30), the sampling distribution of the sample mean will be approximately normally distributed. The mean of the sampling distribution will be equal to the population mean, and the standard deviation will be equal to the population standard deviation divided by the square root of the sample size.

If Random Samples of Size N = 36 Are Drawn