Z-Score Calculator
Calculate z-scores, find raw scores from z-scores, and look up cumulative probabilities using the standard normal distribution.
Mode
Z-Score
1.2
88.49% of values fall below x = 72
| Formula | Expression |
|---|
| Z-score | z = (x − μ) / σ |
| Raw score | x = μ + z · σ |
| Percentile | P = Φ(z) × 100% |
Results
| Property | Value |
|---|
| Raw score (x) | 72 |
| Mean (μ) | 60 |
| Std Dev (σ) | 10 |
| Z-score | 1.2 |
| Percentile (CDF) | 88.49th |
| % of data below x | 88.49% |
| % of data above x | 11.51% |
Z-Score Reference Table
| Z-score | % Below (CDF) | Use |
|---|
| 0 | 50% | |
| 0.5 | 69.15% | |
| 1 | 84.13% | |
| 1.28 | 89.97% | |
| 1.5 | 93.32% | |
| 1.645 | 95% | 90% CI (one-tail) |
| 1.96 | 97.5% | 95% CI (two-tail) |
| 2 | 97.72% | |
| 2.326 | 99% | |
| 2.576 | 99.5% | 99% CI (two-tail) |
| 3 | 99.87% | |
| 3.5 | 99.98% | |