This simulation employed a compiler which explains the role of central limit theorem in dealing with populations that are not normally distributed. A group of 10000-data-point populations were simulated according to five different kinds of distribution: uniform, platykurtic normal, positively-skewed exponential, negatively-skewed triangular, and bimodal. Three 500-data-point sampling distributions of sample sizes of 2, 10, and 30 were created from each population. All populations and sampling distributions were displayed in histograms for analysis along with their means and standard deviations. The results verified the principles of the central limit theorem and indicated that if the population is close to normality, a smaller sample size is needed so that the central limit theorem can take effect. But if the population is far from normality, a large sample size might be required. A proportion of population was proposed for a sample size based on the simulation results. Further studies and implications are discussed.

central limit theorem, sampling distribution, normal distribution, non-normal distributions