### Z-Score Formula

The formula to convert x to z is the following:z = (x - μ) / σ

x : the value being solved for

μ : the average or mean

σ : the standard deviation

### Sample z-score problem

Haley received a 92 on a test. The class average is 76 with a standard deviation of 7. What is the z-score?

z = (92 - 76) / 8

The z-score is: 2.2857

What does this mean?

This value means that Haley's 92 is 2.2857 standard deviations from the mean. If she fell within 2 standard deviations to the right and left of the average score she would have been within 95% of the class scores, but because she is slightly over 2 standard deviations, it can be inferred that she did better than 95% of the class.