The annual incomes of the households in a certain community range between 5 and 25 thousand dollars. Let X represent the annual income (in thousands of dollars) of a household chosen at random in this community, and suppose that the probability density function for X is f (x) = kx, 5 ≤ x ≤ 25.

(a) Find the value of k that makes f (x) a density function.

(b) Find the fraction of households whose income exceeds $20,000.

(c) Find the mean annual income of the households in the community.