Please provide step by step answers:

Dr. Michael Smith, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Michael can vaccinate a dog every 3 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 Michaels vaccination (service) times are negative exponentially distributed. Compute the following:

a. The probability that Michael is idle. [ Select ] [".5", ".12", ".25", ".35"]

b. The average number of dogs being vaccinated and waiting to be vaccinated. [ Select ] ["1", "2", "7", "4"]

c. The average time a dog waits before getting vaccinated. [ Select ] ["4.7", ".15", "3", "4"] minutes

d. The average amount of time a dog spends waiting in line and being vaccinated. [ Select ] ["10", "3", "6", "1.2"] minutes.

Thanks.