Final answer:
The random variable X follows an F-distribution with parameters (16,4), typically used in analysis of variance to compare variances and produce crucial F-statistics for hypothesis testing.
Step-by-step explanation:
The distribution of X, which represents a randomly selected realtor's monthly commission, is given by an F-distribution with parameters (16,4). The F-distribution is used in analysis of variance and is used to compare two variances to find out if they come from populations with the same variance. The shape of the F-distribution is non-symmetric and it is bounded on the left by zero but skewed to the right.
Random variables that follow an F-distribution are commonly used in hypothesis testing and are critical in generating F-statistics, which can determine if there are significant differences between data sets. In this particular application, the distribution of the realtor's monthly commission is determined by comparing variance across multiple groups or samples.