# Normal distribution

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

**Normal distribution** takes special role in the probability theory. This is most common continues 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 equals to mean μ.

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

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### 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) looks like this:

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

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

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