Let X1, X2, X3, X4 represent the random times in days needed to complete four steps of a project. These times are independent and have gamma distributions with and a1 3, a2 2, a3 5, a4 3, respec- common tively. One step must be completed before the next can be started. Let Y equal the total time needed to complete the project.
(a) Find an integral that represents P(Y 25)
(b) Using a normal distribution, approximate the answer to part (a). Is this approach justified?