1. Customers arrive at Rich Dunn's Styling Shop at a rate of 4 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 5 haircuts per hour. a) The average number of customers waiting for haircuts | b) The average number of customers in the shop = c) The average time a customer waits until it is his or her turn= d) The average time a customer spends in the shop = [ e) The percentage of time that Rich is busy | customers (round your response to two decimal places). customers (round your response to two decimal places). minutes (round your response to two decimal places). minutes (round your response to two decimal places). percent (round your response to the nearest whole number). 2. Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 2 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. a) The probability that Tarun is idle = b) The proportion of the time that Tarun is busy [ (round your response to two decimal places). (round your response to two decimal places). dogs (round your response to two decimal places). c) The average number of dogs being vaccinated and waiting to be vaccinated= d) The average number of dogs waiting to be vaccinated=[ e) The average time a dog waits before getting vaccinated [ dogs (round your response to two decimal places). minutes (round your response to two decimal places). 1) The average amount of time a dog spends waiting in line and being vaccinated [ minutes (round your response to two decimal places). 3. Bill Youngdahl has been collecting data at the TU student grill. He has found that, between 5:00 PM. and 7:00 P.M., students arrive at the grill at a rate of 24 per hour (Poisson distributed) and service time takes an average of 2.0 minutes (negative exponential distribution). There is only 1 server, who can work on only 1 order at a time. a) The average number in the line b) The average time in the system = customers (round your response to two decimal places). minutes (round your response to one decimal place). c) Suppose that a second server can be added to team up with the first (and, in effect, act as one faster server). This would reduce the average service time to 90 seconds. The average time in the system | minutes (round your response to two decimal places). d) Suppose a second server is added and the 2 servers act independently, with each taking an average of 2.0 minutes. If a second server is added, the average time a customer spends in the system = minutes (round your response to two decimal places).