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.