Impact of Sample Size on Approximating the Normal Distribution

As the number of samples from a normal probability distribution with a user-defined mean and user-defined standard deviation increases, the more closely the sample probability distribution resembles the theoretical normal probability distribution.
  • Contributed by: Paul Savory (University of Nebraska-Lincoln)


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You can control the specification of a mean, a standard deviation, and the number of samples. The number of samples is randomly generated from the underlying normal distribution with the given mean and standard deviation. This 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 standard deviation, the more closely the sample probability distribution will resemble the theoretical distribution.
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Related Curriculum Standards

US Common Core State Standards, Mathematics