Reference & charts

Normal Distribution Z-Score Table

Z-score table for normal distribution probabilities.

For normally distributed data, z-scores standardize values: z = (x − μ) / σ. Use this table to find the proportion of data below a given z-score.

Selected z-scores and cumulative probabilities (standard normal)

z	Area below	z	Area below
0.0	0.5000	1.0	0.8413
0.5	0.6915	1.5	0.9332
0.67	0.7486	2.0	0.9772
0.84	0.7995	2.5	0.9938
−1.0	0.1587	−2.0	0.0228
−1.96	0.0250	−2.58	0.0049

Empirical rule

For bell-shaped data: ~68% within 1 SD of mean, ~95% within 2 SD, ~99.7% within 3 SD. This connects standard deviation to the normal table.

Calculate your sample mean and SD, convert any value to a z-score, then look up the area in this table to find percentiles.

Find your category or range in the table, then use the linked calculator to compute an exact value for your inputs.

Calculator