Z-Score Table

What is a Z-Score?

A Z-score measures how many standard deviations a value is from the mean of a standard normal distribution (μ = 0, σ = 1). The table gives the cumulative probability Φ(z) = P(Z ≤ z) — the area under the bell curve to the left of z.

• Z = 0: P = 0.5000 — exactly at the mean, 50% of values fall below.
• Negative Z: use symmetry: P(Z ≤ −z) = 1 − P(Z ≤ z).
• Between two values: P(a ≤ Z ≤ b) = Φ(b) − Φ(a).

Common Critical Values

The most frequently used Z-scores in confidence intervals and hypothesis testing.

Standard Normal Distribution Table (Z = 0.0 to 3.4)

Each cell shows P(Z ≤ z) where z = row + column. For example, Z = 1.96 → row 1.9, column 0.06 → 0.9750. For negative Z-scores, use: P(Z ≤ −z) = 1 − P(Z ≤ z).

How to Read This Table

• Find Z = 1.96: go to row 1.9, column 0.06 → read 0.9750.
• Two-tailed 95% CI: the area in both tails = 0.05; each tail = 0.025; so look up the Z where P = 0.9750 → Z = 1.960.
• Negative Z: P(Z ≤ −1.96) = 1 − 0.9750 = 0.0250.
• Area between two Z-scores: P(−1.96 ≤ Z ≤ 1.96) = 0.9750 − 0.0250 = 0.9500 (95%).

References

• Khan Academy — Normal distributions and Z-scores.
• OpenStax — Introductory Statistics, Section 6.1: The Standard Normal Distribution.
• Wikipedia — Standard normal table (definition and usage).

See also