When preparing a bid on a large construction project, a contractor analyzes how long each phase of the construction will take. Suppose that the contractor estimates that the time required for the electrical work will be X hundred worker-hours, where X is a random variable with density function f (x) = x(6 - x)/18, 3 ≤ x ≤ 6. (See Fig. 3.)

(a) Find the cumulative distribution function F (x).

(b) What is the likelihood that the electrical work will take less than 500 worker-hours?

(c) Find the mean time to complete the electrical work.

(d) Find Var (X ).

.5 Y f(x) = 0 x(6 - x) 18 3 Time required Figure 3 Density function for construc- tion bid. X 6