For the situation of Example 5.6.1, calculate the probability that at least 75% of the components last 150 hours when
(a) c = 300, X ~ gamma(a, b), a = 4,b = 5.
(b) c = 100, X ~ gamma(a, b), a = 20, b = 5.
(c) c = 100, X ~ gamma(a,b), a = 20.7, b = 5.
(In parts (a) and (b) it is possible to evaluate the gamma integral in closed form, although it probably isn't worth the effort in (b). There is no closed-form expression for the integral in part (c), which has to be evaluated through either numerical integration or simulation.)