# Normal distribution

Plots the CDF and PDF graphs for normal distribution with given mean and variance.

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/4986/. Also, please do not modify any references to the original work (if any) contained in this content.

**Normal distribution** takes a unique role in the probability theory. This is the most common continuous probability distribution, commonly used for random values representation of unknown distribution law.

#### Probability density function

Normal distribution probability density function is the Gauss function:

where μ — mean,

σ — standard deviation,

σ ² — variance,

Median and mode of Normal distribution equal to mean μ.

The calculator below gives probability density function value and cumulative distribution function value for the given x, mean, and variance:

#### Cumulative distribution function

Normal distribution cumulative distribution function has the following formula:

where, erf(x) - error function, given as:

#### Quantile function

Normal distribution quantile function (inverse CDF) given as inverse error function:

p lays in the range [0,1]

Standard normal distribution quantile function (σ =1, μ=0) equates like this:

This function is called **the probit function**.

The calculator below gives quantile value by probability for the specified through mean and variance normal distribution( set variance=1 and mean=0 for probit function).

#### Similar calculators

- • Binomial distribution, probability density function, cumulative distribution function, mean and variance
- • Log-normal distribution
- • Student t-distribution
- • Hypergeometric Distribution. Probability density function, cumulative distribution function, mean and variance
- • Geometric Distribution. Probability density function, cumulative distribution function, mean and variance
- • Math section ( 262 calculators )

**CDF Distribution Distribution function Gauss distribution Math Mean Normal distribution PDF Probability dencity Probability density probability theory Quantile Quantile function Statistics Variance

**

**PLANETCALC, Normal distribution

## Comments