A worked example
A score of 85 with a mean of 75 and a standard deviation of 10 has a z-score of 1.0 — roughly the 84th percentile.
Frequently asked questions
What does a z-score of 0 mean?
The value is exactly equal to the mean — neither above nor below average.
Why does the percentile assume a normal distribution?
The relationship between a z-score and a percentile relies on the bell-curve shape of the normal distribution — if the underlying data is skewed or follows a different distribution, the same z-score corresponds to a different actual percentile.
What's a 'typical' range for z-scores?
About 68% of values in a normal distribution fall within ±1, about 95% fall within ±2, and about 99.7% fall within ±3 — z-scores beyond ±3 are relatively rare under a normal distribution.