The life times, in hours, of a random sample of 25 electronic components yield sample mean X = 113.5 hours and sample variance S2 = 1205.55 hours2. Find model-based estimators of the 95th population percentile of the lifetime distribution, and of the probability that a randomly selected component will last more than 140 hours, under the following two model assumptions:

(a) The distribution of life times is Weibull(α, β). (See Exercise 14 in Section 3.5 for the definition of this distribution.)

(b) The distribution of life times is exponential(λ).