Let X1, X2, X3, X4 represent the random times in days needed to complete four steps of a
Chapter 5, Problem 5.6-15(choose chapter or problem)
Let \(X_1, X_2, X_3, X_4\) represent the random times in days needed to complete four steps of a project. These times are independent and have gamma distributions with common \(\theta = 2\) and \(\alpha_1 = 3\), \(\alpha_2 = 2\), \(\alpha_3 = 5\), \(\alpha_4 = 3\), respectively. 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 \(P(Y \le 25)\).
(b) Using a normal distribution, approximate the answer to part (a). Is this approach justified?
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