Normal Curve & z-Scores

Set the mean and standard deviation, pick a raw score, and read off its z-score and percentile. The shaded area is the proportion of scores in your selected region.

Raw score x100

z-score0.00

Shaded area50.0%

mean μ 100

std dev σ 15

raw score x 100

region

Empirical (68–95–99.7) rule: about 68% of scores fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean.

Try: set the region to "within ±z" and drag x to exactly one σ above the mean (z = 1.00) — the shaded area reads ~68%, the empirical rule. Then switch to "Area to the LEFT" to see the ~84th percentile.