Suppose the service time, in minutes, at a bank has the Exponential distribution with 2 = 1/2. Determine the exact distribution of the average time to service for the first n customers, when n = 16,...

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Extracted text: Suppose the service time, in minutes, at a bank has the Exponential distribution with 2 = 1/2. Determine the exact distribution of the average time to service for the first n customers, when n = 16, 36, 100. (Hint: use the mgf.) Then use the pgamma function in R to find the exact probability and compare it to the normal approximation.