FORMULA
Z = (X − μ) / σ
"Distance from mean, measured in standard deviations"
POSITIVE Z
Above the mean
X > μ → z is positive. You scored higher than average.
NEGATIVE Z
Below the mean
X < μ → z is negative. You scored lower than average.
PERCENTILE
normalcdf(−∞, z)
% of values AT OR BELOW a given z-score.
EMPIRICAL RULE
68 — 95 — 99.7
Within ±1, ±2, ±3 standard deviations of the mean.
COMPARE SCORES
Higher z = better
Compare z-scores across different tests to find the relative winner.