Let X = the time (in 10-1 weeks) from shipment of a defec- tive product until the customer returns the product. Suppose that the minimum return time is y = 3.5 and that the excess X-3.5 over the minimum has a Weibull distribution with parameters a 2 and 1.5 (see "Practical Applications of the Weibull Distribution," Industrial Quality Control, Aug. 1964: 71-78).

a. What is the cdf of X?

b. What are the expected return time and variance of return time? [Hint: First obtain E(X-3.5) and V(X-3.5).]

c. Compute P(X> 5).

d. Compute P(5 X 8).