How to Use the Z-Score & Standard Normal Distribution Calculator
-
1
Enter your raw score $x$, population mean $\mu$, and standard deviation $\sigma$.
-
2
The calculator computes the standard $z$-score: $z = \frac{x - \mu}{\sigma}$.
-
3
Review the cumulative probability $P(Z < z)$ (percentile rank), right-tail probability $P(Z > z)$, and two-tailed probability.
-
4
Inspect the shaded bell curve canvas highlighting your exact standard deviation position.
Practical Example & Use Case
Common Real-World Scenario
A student scoring 130 on an IQ test (mean 100, SD 15) has a $z$-score of +2.00, placing them in the 97.72nd percentile ($P < 130 = 0.9772$).
Technical Notes & Limitations
Browser Engine Architecture
Calculates standard normal cumulative distribution using the polynomial error function approximation with precision within $10^{-7}$.
Frequently Asked Questions
What does a z-score of 0 mean?
A z-score of 0 indicates that the raw score is exactly equal to the mean average of the population.