Dr$.$ Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun 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 Tarun$$s vaccination $($service$)$ times are negative exponentially distributed. Compute the following:

The probability that Tarun is idle.

$\mathrm{.}25$

The average number of dogs being vaccinated and waiting to be vaccinated.

$1$

The average time a dog waits before getting vaccinated.

$3$

minutes

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

$[$ Select $]$

minutes