normcdf (Statistics Toolbox)

Normal cumulative distribution function (cdf)

Syntax

```
P = normcdf(X,MU,SIGMA)
```

Description

normcdf(X,MU,SIGMA) computes the normal cdf at each of the values in X using the corresponding parameters in MU and SIGMA. Vector or matrix inputs for X, MU, and SIGMA must all have the same size. A scalar input is expanded to a constant matrix with the same dimensions as the other inputs. The parameters in SIGMA must be positive.

The normal cdf is

The result, p, is the probability that a single observation from a normal distribution with parameters µ and will fall in the interval (- x].

The standard normal distribution has µ= 0 and = 1.

Examples

What is the probability that an observation from a standard normal distribution will fall on the interval [-1 1]?

p = normcdf([-1 1]);
p(2) - p(1)
ans =
    0.6827

More generally, about 68% of the observations from a normal distribution fall within one standard deviation, , of the mean, µ.

nlpredci normfit