If random samples of size n = 36 are drawn from a non-normal population with finite mean = 75 and standard deviation = 15, then the sampling distribution of the sample mean is approximately normally distributed with mean = 75 and standard deviation = 2.5.

Question

If random samples of size n = 36 are drawn from a non-normal population with finite mean  = 75 and standard deviation  = 15, then the sampling distribution of the sample mean  is approximately normally distributed with mean  = 75 and standard deviation  = 2.5.

Quizplus · Accepted Answer

This is a well-known result of the central limit theorem, which states that for large enough sample sizes, the sampling distribution of the sample mean will be approximately normal regardless of the underlying population distribution. The mean and standard deviation of this sampling distribution can be calculated using formulas and are given in the question.

If Random Samples of Size N = 36 Are Drawn