Sam Certo, 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:
- The probability that Sam is idle.
- The proportion of the time that Sam is busy.
- The average number of dogs being vaccinated and waiting to be vaccinated.
- The average number of dogs waiting to be vaccinated.
- The average time a dog waits before getting vaccinated.
- The average amount of time a dog spends waiting in line and being vaccinated.