Mistake Master
Three Distributions Are in Play, and Only One of Them Goes Normal
You'll learnto keep the population, one sample, and the sampling distribution of a statistic apart, why the sample mean centers on μ with spread σ/√n, what the Central Limit Theorem does and does not promise, and which standard deviation belongs under a z.
A shop logs how many days each repair takes, and the log leans hard to the left: most jobs are quick and a few drag on. Sample it and three different distributions are on the table at once. The population has a shape that sampling never touches. One sample of a hundred repairs rebuilds that same skyline, and a bigger sample shows the skew more clearly rather than less. And the sample mean, filed across every possible sample, is a third picture entirely — centered exactly on the population mean, narrower by a factor of the square root of n, and, this being the theorem, near enough normal whatever the population looks like. This animation builds that third pile by counting every sample rather than drawing any, watches the skew drain out of it, and ends on the exam’s favourite fork: the same 12.2 ounces asked of one bottle and of an average of sixteen, two answers a factor of thirteen apart. Twelve short steps; press Next for each one.