Standard Normal Calculator — Formule
## Standard Normal Distribution
### PDF Formula
**phi(z) = (1 / sqrt(2*pi)) * e^(-z^2/2)**
The standard normal distribution has mean 0 and standard deviation 1. It is the reference distribution for z-scores and hypothesis testing. The PDF is symmetric around z=0, meaning phi(z) = phi(-z). Common critical values: z = 1.645 (90%), 1.96 (95%), 2.576 (99%).
### PDF Formula
**phi(z) = (1 / sqrt(2*pi)) * e^(-z^2/2)**
The standard normal distribution has mean 0 and standard deviation 1. It is the reference distribution for z-scores and hypothesis testing. The PDF is symmetric around z=0, meaning phi(z) = phi(-z). Common critical values: z = 1.645 (90%), 1.96 (95%), 2.576 (99%).
Exemple Résolu
Find the PDF value at z = 1.96 (the 95% critical value).
- phi(1.96) = (1 / sqrt(2*pi)) * e^(-1.96^2 / 2)
- = 0.39894 * e^(-1.9208)
- = 0.39894 * 0.14634
- = 0.05844