Calculateur de Distribution Normale — Formule
## How to Use the Normal Distribution
### PDF Formula
**f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-0.5 * ((x - mu)/sigma)^2)**
The normal (Gaussian) distribution is the most important continuous distribution in statistics. It is defined by its mean (mu) and standard deviation (sigma). The z-score standardizes any value to units of standard deviations from the mean.
### PDF Formula
**f(x) = (1 / (sigma * sqrt(2*pi))) * e^(-0.5 * ((x - mu)/sigma)^2)**
The normal (Gaussian) distribution is the most important continuous distribution in statistics. It is defined by its mean (mu) and standard deviation (sigma). The z-score standardizes any value to units of standard deviations from the mean.
Exemple Résolu
Test scores have mean 70 and SD 10. Find the z-score and PDF for a score of 75.
- Z = (75 - 70) / 10 = 0.5
- The score is 0.5 standard deviations above the mean
- PDF = (1 / (10 * sqrt(2*pi))) * e^(-0.5 * 0.25)
- = 0.03989 * 0.8825 = 0.03521
- Variance = 10^2 = 100