The Central Limit Theorem is a fundamental theorem of probability and describes the characteristics of the population of the means. According the Central Limit Theorem, the sample mean will be normally distributed regardless of the population distribution. Regardless of the distribution of parent.

The Central Limit Theorem tells us what happens when we have the sum of a large number of independent random variables each of which contributes a small amount to the total.

The following video provides a good introduction to the central limit theorem and the sampling distribution of the mean.