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1. You are running a ticketing booth. There are three agents and each agent is able to serve 1/6 customer per minute (i.e., 10 customers per hour) and their service times are exponentially distributed. Customers arrive at the rate of 21/60 customer per minute and inter-arrival times are exponentially distributed. You have two lines, Line A and Line B. Line A is tendered by two agents and B is by one agent. Upon their arrivals customers are randomly routed to two lines. That is, with probability 2/3 customers are sent to Line A and with probability 1/3 customers are sent to Line B. (Let us assume that customers are not complaining about this random split.) What is the average wait time of customers at your ticketing booth? (It is possible that your answer is not one of the choices. I believe that it is because of your rounding ups or rounding downs during your calculations. If so, select the choice that is closest to your calculated number.) a)5.96 minutes per customer b) 3.47 minutes per customer c)8.64 minutes per customer d)14 minutes per customer e)9.98 minutes per customer 2. (Continued from Question 1) After a while, customers argue that the random split is not fair. You want to revise the splitting probability (which was 2/3 to Line A and 1/3 to Line B) to make sure that the average wait time per customer from each line is the same. What will be the probability of sending a customer to Line A after the revision? a. The probability is greater than or equal to 90%. b. The probability is greater than or equal to 30% and less than 50%. c. The probability is greater than or equal to 50% and less than 70%. d. The probability is less than 30%. e. The probability is greater than or equal to 70% and less than 90%.