A variable x of a finite population has the following frequency distribution:

x 578 f 25 40 60 Suppose a member is selected at random from the population and let X denote the value of the variable x for the member obtained.

a. Determine the probability distribution of the random variable X.

b. Use random-variable notation to describe the events that X takes on the value 6, a value of at most 6, and a value greater than 6.

c. Find P(X = 6), P(X ≤ 6), and P(X > 6). Interpret your results.

d. Construct a probability histogram for the random variable X.