Central Limit Theorem in a Skewed Leptokurtic Distribution

Abstract

According to the central limit theorem, the distribution of the sample mean is approximately normal if the sample size, n, is sufficiently large, regardless of original data distribution. However there seems to be a difference in opinion on how large n should be. Some books said that n = 25 is sufficient enough while some considered n = 30 to be sufficient. This paper investigates the size of n that would allow us to apply the central limit theorem when samples taken are from a population