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# stats::normalCDF

Cumulative distribution function of the normal distribution

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```stats::normalCDF(m, v)
```

## Description

stats::normalCDF(m, v) returns a procedure representing the cumulative distribution function

of the normal distribution with mean m and variance v.

The procedure f := stats::normalCDF(m, v) can be called in the form f(x) with an arithmetical expression x. The value 1/2 + 1/2* erf((x - m)/sqrt(2*v)) is returned.

If x is a floating-point number and both m and v can be converted to floating-point numbers, this value is returned as a floating-point number. Otherwise, a symbolic expression is returned.

Numerical values for m and v are only accepted if they are real and v is positive.

## Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision.

## Examples

### Example 1

We evaluate the cumulative distribution function with mean m = 2 and variance at various points:

```f := stats::normalCDF(2, 3/4):
f(-infinity), f(-3), f(PI), f(infinity)```

`f(-100.0), f(-3.0), f(float(PI)), f(10.0), f(100.0)`

`delete f:`

### Example 2

We use symbolic arguments:

`f := stats::normalCDF(m, v): f(3), f(x)`

When numerical values are assigned to m and v, the function f starts to produce numerical values:

`m := 4: v := PI: f(3), f(3.0)`

`delete f, m, v:`

## Parameters

 m The mean: an arithmetical expression representing a real value v The variance: an arithmetical expression representing a positive real value