Use repeated random sampling data from a variety of distributions and a range of sample sizes to examine the approximate standard normality of (X̄ − μ)/(s/√n) for large samples (n ≥ 30), where s is the sample standard deviation (Central limit theorem).

u4-t5-s1-d4

Interactive

Does (x̄ − μ)/(s/√n) look standard normal?

manipulative

Sample from a skewed population, standardise each sample mean, and watch the z histogram settle on N(0,1) as n grows — the CLT in action.

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