Standard Normal Distribution (z-table)

The table below gives the standard normal deviate z corresponding to a range of two-tailed P values. A two-tailed P value is the probability that a standard normal variable exceeds z in absolute value — that is, P = Pr(|Z| > z). Commonly used critical values are z = 1.960 for P = 0.05 and z = 2.576 for P = 0.01.

P	z	P	z
0.0001	3.891	0.10	1.645
0.0002	3.719	0.12	1.555
0.0003	3.615	0.14	1.476
0.0004	3.540	0.16	1.405
0.0005	3.481	0.18	1.341
0.0006	3.432	0.20	1.282
0.0007	3.390	0.22	1.227
0.0008	3.353	0.24	1.175
0.0009	3.320	0.26	1.126
0.001	3.291	0.28	1.080
0.002	3.090	0.30	1.036
0.003	2.968	0.32	0.994
0.004	2.878	0.34	0.954
0.005	2.807	0.36	0.915
0.006	2.748	0.38	0.878
0.007	2.697	0.40	0.842
0.008	2.652	0.42	0.806
0.009	2.612	0.44	0.772
0.01	2.576	0.46	0.739
0.02	2.326	0.48	0.706
0.03	2.170	0.50	0.674
0.04	2.054	0.60	0.524
0.05	1.960	0.70	0.385
0.06	1.881	0.80	0.253
0.07	1.812	0.90	0.126
0.08	1.751	1.00	0.000
0.09	1.695

The z-score

A z-score expresses how many standard deviations a value $X$ lies above or below the population mean $\mu$. It is calculated as:

$$ z = \frac{X - \mu}{\sigma} $$

where $\sigma$ is the population standard deviation. Because any normally distributed variable can be converted to a z-score, the table above applies to all such variables regardless of their original scale or units. To find the two-tailed probability associated with an observed z-score, locate the closest value in the z column and read off the corresponding P value.