An example taken from "Statistical Inference, @ed: by casella and berger.

A manufacturer is interested in determining the probability that, out of c components, at least t of them will last h hours. Suppose the component is modeled by a gamma distribution. Find the following:

(a) c=300, X~Gamma(a,b), a=4, b=25, t=100 hours, 50% survive

(b) c=100, X~Gamma(a,b), a=20, b=5, t=100 hours, 50% survive

(c) c=100, X~Gamma(a,b), a=20.7, b=5, t=100 hours, 50% survive

The generation is to be done with SAS or R programming.