Was this calculator helpful?
Common invNorm Values (Standard Normal)
| Probability (p) | Z-Score (invNorm) | Common Use |
|---|---|---|
| 0.900 | 1.282 | 90% confidence (one-tailed) |
| 0.950 | 1.645 | 95% confidence (one-tailed) |
| 0.975 | 1.960 | 95% CI (two-tailed, each side) |
| 0.990 | 2.326 | 99% confidence (one-tailed) |
| 0.995 | 2.576 | 99% CI (two-tailed, each side) |
| 0.9995 | 3.291 | 99.9% CI (two-tailed) |
Frequently Asked Questions
The inverse normal distribution (also called the quantile function or probit function) finds the z-score or x-value that corresponds to a given cumulative probability. For example, if you want the value below which 95% of a normal distribution falls, the inverse normal gives you that value.
The normal CDF takes a z-score and returns a probability (area under the curve to the left). The inverse normal does the opposite — it takes a probability and returns the z-score. If normalcdf(z) = 0.975, then invNorm(0.975) = 1.96.
On a TI-84: press 2nd → VARS (DISTR) → scroll to invNorm( → enter (probability, mean, standard deviation). For example, invNorm(0.95, 0, 1) gives 1.645, which is the z-score with 95% of the distribution to its left.
invNorm(0.95) = 1.6449. This means 95% of a standard normal distribution falls below a z-score of 1.645. It's commonly used in statistics for one-tailed 95% confidence intervals and hypothesis testing.
For a 95% confidence interval (two-tailed), the critical z-score is ±1.96. This comes from invNorm(0.975) = 1.96, which leaves 2.5% in each tail. For a 99% CI, the critical z is ±2.576 (invNorm(0.995)).
The inverse normal is used in: finance (Value at Risk calculations), quality control (finding defect thresholds), medicine (clinical trial confidence intervals), psychology (percentile scoring on standardized tests), and engineering (reliability analysis and failure rate thresholds).