The normal distribution and z-scores

A z-score counts how many standard deviations a value sits from the mean. About 68/95/99.7% lie within 1/2/3 of them.

A worked example

A time of 52 s with mean 40 s and standard deviation 5 s gives z = (52 − 40) / 5 = 2.4.

The mistake people actually make

A percentile is a rank within the group, not a mark out of 100. A 95% confidence level describes the method, not one interval.

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