Normality for nonnormal distributions

Koh, Khong Liang

Abstract

It has been usually assumed that a sample data is normally distributed when the sample size is at least 30. This is the general rule in using central limit theorem based on the sample size being greater or equal to 30. Many literary works also assumed normality when sample size is at least 30. This study aims to determine the least required sample size that satisfy normality assumption from three non-normal distributions, Poisson, Gamma and Exponential distributions. Computer simulations are carried out to study the least required sample size for the three distributions. Through the study, it is found that sample data from Poisson and Gamma distributions need sample size less than 30, while Exponential needs more than 30 to achieve normality.

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