What is a Z-score?
A z-score is the number of standard deviations a value lies above or below the mean. Z = (x − μ) ÷ σ. The "Z-table" gives the area under the standard normal curve (μ = 0, σ = 1) up to a given z — i.e. P(Z ≤ z).
Common z-scores
| Z | P(Z ≤ z) | Common use |
|---|---|---|
| 1.282 | 0.9000 | 90% confidence (one-tail) |
| 1.645 | 0.9500 | 95% confidence (one-tail) |
| 1.960 | 0.9750 | 95% confidence (two-tail) |
| 2.326 | 0.9900 | 99% confidence (one-tail) |
| 2.576 | 0.9950 | 99% confidence (two-tail) |
| 3.000 | 0.9987 | ~3-sigma |
FAQ
How is the area computed?
Using the Abramowitz-Stegun rational approximation to erf(x), accurate to ~7 decimal places — more precise than printed Z-tables.
How is the inverse computed?
Using Beasley-Springer-Moro inverse normal — accurate to ~6 significant figures across the typical 0.0001 to 0.9999 range.