Will runs a dog grooming service, and has asked you to analyze the current 'line situation....

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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. How long, on average, will a dog wait for grooming? In total, how long will a dog spend in the shop waiting and being groomed? 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? Will wants to reduce the wait time, and is considering two options. The first would be to hire a helper, who would assist Will, and reduce the grooming time from 10 minutes to 8 minutes. (NOTE: The helper only helps, and does not work alone.) What would the wait time be with a helper? 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? 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. How long, on average, will a dog wait for grooming? In total, how long will a dog spend in the shop waiting and being groomed? 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? Will wants to reduce the wait time, and is considering two options. The first would be to hire a helper, who would assist Will, and reduce the grooming time from 10 minutes to 8 minutes. (NOTE: The helper only helps, and does not work alone.) What would the wait time be with a helper? 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?