*(Updated July 17, 2013)*

If a body of data is normally distributed (i.e., follows the bell-shaped curve), we can convert an individual's

*z*-score on a given variable into a percentile. A percentile refers to the percentage of sample members an individual stands above on the variable.

If we look at page 26 of

*Naked Statistics*, we can translate any particular

*z*-score into a percentile (again, as long as the distribution is normal). For instance, we can see that a

*z*-score of +1 (shown along the bottom of the diagram in the book as mu + 1 sigma) places someone at roughly the 84th percentile. Fifty percent of the sample lies below mu, and another 34.1% lie between mu and mu +1 sigma, thus adding up to 84.1.

On this webpage, you can see how

*z*-scores and percentiles correspond to areas under the normal curve. There is also a website where you can simply type in a

*z*-score and get the corresponding percentile.

This photo of the board from a recent class meeting (thanks to Kristina) summarizes some of the major properties of

*z*-scores.