Industrial and Management Systems Engineering



Impact of Sample Size on Approximating the Normal Distribution

Date of this Version



P. Savory (2010), “Sample Size Impact on Approximating the Normal Distribution”, Mathematica Software Demonstration, The Wolfram Demonstations Project. Available at:


As the number of samples from a normal probability distribution with a user-defined mean and user-defined variance increases, the more closely the sample probability distribution resembles the theoretical normal probability distribution. User controls allow for the specification of a mean, a variance, and the number of samples. The number of samples is randomly generated from the underlying Normal distribution with the given mean and variance. The Mathematica demonstration compares the sample probability distribution with the theoretical Normal distribution. As probability and statistical theory show us, as the number of samples increase for the given mean and variance, the more closely the sample probability distribution will resemble the theoretical distribution.