Inverse Normal Distribution Calculator
Enter a cumulative probability to obtain the corresponding z-score or value from a normal distribution with mean μ and standard deviation σ.
Z-score: 1.6449
Value: 1.6449
Two-sided central interval (1 − α, α = 0.050): (-1.9600, 1.9600)
How to Use This Calculator
- Enter the mean and standard deviation of your normal distribution.
- Supply a cumulative probability between 0 and 1 (exclusive).
- Read off the corresponding z-score and value on the specified normal distribution.
- Use the reported two-sided interval for confidence level interpretation.
Formula
Z = Φ−1(p)
X = μ + σZ
Φ−1 denotes the inverse cumulative distribution function (quantile function) of the standard normal distribution.
Frequently Asked Questions
What happens if p = 0 or p = 1?
The extremes correspond to −∞ and +∞. Numerically, restrict p to (0, 1) for finite z-scores.
How precise is this approximation?
The Acklam algorithm is accurate to better than 1e−9 across most of the distribution.
Can I compute quantiles for other distributions?
This tool focuses on the normal distribution. Use specialized calculators for other distributions.