normcdf (Statistics Toolbox)

Normal cumulative distribution function (cdf).

Syntax

P = normcdf(X,MU,SIGMA)

Description

normcdf(X,MU,SIGMA) computes the normal cdf with parameters MU and SIGMA at the values in X. The arguments X, MU and SIGMA must all be the same size except that scalar arguments function as constant matrices of the common size of the other arguments.

The parameter 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.

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