The F-distribution is a continuous sampling distribution of the ratio of two independent random variables with chi-square distributions, each divided by its degrees of freedom. The F-distribution is right skewed and described by its numerator (ν_{1}) and denominator (ν_{2}) degrees of freedom. The following plots show the effect of different values of degrees of freedom on the shape of the distribution.

Use the F-distribution when a test statistic is the ratio of two variables that each have a chi-square distribution. For example, use the F-distribution in the analysis of variance and in hypothesis testing to determine whether two population variances are equal.

Suppose X follows an F-distribution with 5 numerator degrees of freedom and infinite denominator degrees of freedom, and you want the probability that X is less than or equal to 2. You can find the probability that Y is less than or equal to 2, where Y follows an F-distribution with 5 numerator and 99999 denominator degrees of freedom and Y approximates X.

- Choose .
- In Numerator degrees of freedom, enter
`5`. - In Denominator degrees of freedom, enter
`99999`. - Choose Input constant and enter
`2`. Click OK.

The CDF for 2 is 0.924755. This value gives the area under the curve up to 2.