Will runs a dog grooming service, and has asked you to analyze the current 'line situation'. he has gathered data and calculated that he can groom a dog in about 10 minutes, based on a negative exponential distribution. he also noted that about 3 dogs arrive to his shop per hour, during all operating hours, based on a poisson distribution. a) how long, on average, will a dog wait for grooming? b) in total, how long will a dog spend in the shop waiting and being groomed? c) will's shop is fairly small, and he only has space for 3 dogs to be in the shop before it gets crowded. what is the probability that there will be more than 3 dogs at any time? d) will wants to reduce the wait time, and is considering two options. the first would be to hire a , who would assist will, and reduce the the grooming time from 10 minutes to 8 minutes. (the only , and does not work alone.) what would the wait time be with a ? the second option is to rent an auto-groomer, a new machine that would allow will to groom a dog in a constant 9 minutes. what would the wait time be with auto-groomer? assuming both options cost the same amount and all else is equal, which should will choose to deliver the shortest wait time?