# Normal distribution

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

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**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).

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

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**PLANETCALC, Normal distribution

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