Question 1

What is the inverse normal distribution?

Accepted Answer

The inverse normal distribution (also called the quantile function or probit function) reverses the normal CDF. Instead of asking 'what is the probability below this value?', it asks 'what value has this probability below it?' For example, the inverse of 0.975 in the standard normal is 1.96, the familiar z-score used in 95% confidence intervals.

Question 2

Why can I only enter probabilities between 0 and 1?

Accepted Answer

The normal distribution extends to negative and positive infinity. A probability of 0 would correspond to negative infinity, and 1 would correspond to positive infinity. In practice, values very close to 0 or 1 (like 0.0001 or 0.9999) still produce finite z-scores, but exactly 0 and 1 are undefined.

Question 3

How is this related to confidence intervals?

Accepted Answer

Confidence intervals use the inverse normal to find critical values. For a 95% confidence interval, you need the z-score where 97.5% of the distribution falls below (because 2.5% is in each tail). That gives z = 1.96. For 99% confidence, you need the 99.5th percentile, giving z = 2.576.

Question 4

How accurate is this calculator?

Accepted Answer

This calculator uses the Beasley-Springer-Moro rational approximation algorithm, which provides accuracy to at least 6 significant digits across the full range of probabilities. For most statistical applications, this exceeds the precision needed.

Probability	Z-Score	Use Case
0.90	1.2816	90% CI lower z
0.95	1.6449	One-tailed 5% significance
0.975	1.9600	95% CI / two-tailed 5%
0.99	2.3263	One-tailed 1% significance
0.995	2.5758	99% CI / two-tailed 1%

Inverse Normal Distribution Calculator

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