Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school.Sam 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 1 dog every 4 minutes, according to a Poisson distribution.Also assume that Sam's vaccinating times are exponentially distributed.
(a)Find the probability that Sam is idle.
(b)Find the proportion of time that Sam is busy.
(c)Find the average number of dogs receiving or waiting to be vaccinated.
(d)Find the average number of dogs waiting to be vaccinated.
(e)Find the average time a dog waits before getting vaccinated.
(f)Find the average amount (mean)of time a dog spends between waiting in line and getting vaccinated.

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The Answer of Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school.Sam 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 1 dog every 4 minutes, according to a Poisson distribution.Also assume that Sam's vaccinating times are exponentially distributed.
(a)Find the probability that Sam is idle.
(b)Find the proportion of time that Sam is busy.
(c)Find the average number of dogs receiving or waiting to be vaccinated.
(d)Find the average number of dogs waiting to be vaccinated.
(e)Find the average time a dog waits before getting vaccinated.
(f)Find the average amount (mean)of time a dog spends between waiting in line and getting vaccinated.

Sam the Vet Is Running a Rabies Vaccination Clinic for Dogs