Suppose you are the 3rd customer waiting in line, and when a customer gets to the front of the line the average service time is 4 minutes for one customer. You will be finished once your service is complete.

Assume customers are served sequentially (back-to-back), that service times of customers are independent, and that service time per customer is an Exponential random variable. If these assumptions are correct, what is the probability you will be finished within 8 minutes? Give the probability in decimal form, rounded to 3 places.

Hint: to get the answer, use the logical "trick" inherent in Poisson processes. You use Poisson probability to get the answer. But first, rephrase the event as a statement about how many "arrivals" occur during the fixed 8 minutes. If you do, in fact, get served within 8 minutes, what is true about how many services occured during the 8 minutes?