A Nanaimo vet, is running a rabies vaccination clinic for dogs at the local grade school. Sam can "shoot" 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 Sam's shooting times are exponentially distributed.

Compute the following:

a) The probability that Sam is idle.

b) The proportion of the time that Sam is busy.

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.

f) The average amount of time a dog spends waiting in line and being vaccinated.

Please show formula's and calculations.