Water Resources HubFree calculator
Normal Distribution — Z-Scores & Probabilities
Enter the mean and standard deviation of your normal distribution, pick the probability you want, and the calculator returns the z-score(s) and the probability — the same steps the FE expects you to do with a standard normal table.
z = (x − μ)/σ
| z | standard score: standard deviations from the mean |
| μ | population mean |
| σ | population standard deviation (must be positive) |
| Φ(z) = P(Z < z) | standard normal cumulative probability, computed here via the error function |
P(X > x) = 1 − Φ(z); P(a < X < b) = Φ(zb) − Φ(za).
For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook.