William W. answered • 06/16/22
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Math and science made easy - learn from a retired engineer
Z-scores are related to the standard deviation and how far away you are from the mean.
Example: Let's say you are weighing widgets. You gather data from weighing a bunch of the widgets and determine the weights are normally distributed with a mean of 44 grams and you calculate the standard deviation as 2 grams. Now, you pick up one widget and weigh it at 47.5 grams and you are asked to find the z-score of that measurement.
mean = μ = 44
standard deviation = σ = 2
observed value = x = 47.5
z = (47.5 - 44)/2 = 1.75
