How to use z-scores

Z-scores are a standardized measure of how many standard deviations a given data point is away from the mean of its data set, given that the data set follows a standard normal distribution.

x is the value we choose.
µ is the mean of the distribution.
σ is the standard deviation of the distribution.

We find the p-value ("probability"-value) associated with the z-score in this table.

That p-value refers to the area under the standard normal distribution (a.k.a. z-distribution) to the left of our z-score!

Z-score = 0.33

p-value = 0.6293 or 62.93%

This means that 62.93% of the area under the standard normal distribution occurs to the left of our z-score!

Created with Statistics Kingdom

A z-score of +0.33 means our data point (x) lies 0.33 standard deviations (σ) to the right of the mean (µ)!

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