Normal Distribution Calculator

Calculate the probability density function (PDF) value and key properties of the normal distribution for a given x, mean, and standard deviation.

Z-Score

0.500000

PDF f(x)0.03520653
Deviations from Mean0.5000
Variance100.0000

Z-Score vs Value (x)

सूत्र देखें →

सूत्र

## 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.

हल किया गया उदाहरण

Test scores have mean 70 and SD 10. Find the z-score and PDF for a score of 75.

  1. 01Z = (75 - 70) / 10 = 0.5
  2. 02The score is 0.5 standard deviations above the mean
  3. 03PDF = (1 / (10 * sqrt(2*pi))) * e^(-0.5 * 0.25)
  4. 04= 0.03989 * 0.8825 = 0.03521
  5. 05Variance = 10^2 = 100