Evaluates the standard normal (Gaussian) distribution function.

Synopsis

#include <imsls.h>

float imsls_f_normal_cdf (float x)

The type double function is imsls_d_normal_cdf.

Required Arguments

float x   (Input)
Point at which the normal distribution function is to be evaluated.

Return Value

The probability that a normal random variable takes a value less than or equal to x.

Description

Function imsls_f_normal_cdf evaluates the distribution function, Φ, of a standard normal (Gaussian) random variable as follows:

The value of the distribution function at the point x is the probability that the random variable takes a value less than or equal to x.

The standard normal distribution (for which imsls_f_normal_cdf is the distribution function) has mean of 0 and variance of 1. The probability that a normal random variable with mean μ and variance σ2 is less than y is given by imsls_f_normal_cdf evaluated at (y − μ)/σ.

Figure 11-5   Plot of Φ(x)

Example

Suppose X is a normal random variable with mean 100 and variance 225. This example finds the probability that X is less than 90 and the probability that X is between 105 and 110.

#include <imsls.h>

main()
{
    float      p, x1, x2;

    x1  = (90.0-100.0)/15.0;
    p   = imsls_f_normal_cdf(x1);
    printf("The probability that X is less than 90 is %6.4f\n", p);

    x1 = (105.0-100.0)/15.0;
    x2 = (110.0-100.0)/15.0;
    p  = imsls_f_normal_cdf(x2) - imsls_f_normal_cdf(x1);
    printf("The probability that X is between 105 and 110 is %6.4f\n",
        p);
}

Output

The probability that X is less than 90 is 0.2525
The probability that X is between 105 and 110 is 0.1169

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