Given a sample from a real-valued probability distribution, the Z-score is a measure of how this sample is from the average (mean), relative to the distribution's standard deviation. It is defined as (Sample-Mean)/(Standard Deviation).
For instance, on an exam with a mean grade of 85, and a standard deviation of 5, a grade of 92 has a Z-score of (92-85)/5=+1.4, while a grade of 70 has a Z-score of (70-85)/5=-3.
Given some normal distribution with an arbitrary mean and standard deviation, the Z-scores of all the samples make up a standard normal distribution (with mean=0 and standard deviation=1).
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