Dr$.$ Tarun$$ Gupta, a Michigan$$ vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can$$ "shoot" a dog every $2$ minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every $5$ minutes according to a Poisson distribution. Also assume that$$ Tarun's shooting times are negative exponentially distributed.

Part $2$

$$a$)$ The probability that Tarun is idle$=0\mathrm{.}60\mathrm{.}6($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ The proportion of the time that Tarun is busy$=0\mathrm{.}40\mathrm{.}4($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ The average number of dogs being vaccinated and waiting to be vaccinated$=0\mathrm{.}660\mathrm{.}66$ dogs$($round your response to two decimal$$ places$).$

Part $5$

$$d$)$ The average number of dogs waiting to be vaccinated$=0\mathrm{.}260\mathrm{.}26$ dogs$($round your response to two decimal$$ places$).$

Part $6$

$$e$)$ The average time a dog waits before getting vaccinated$=0\mathrm{.}10\mathrm{.}1$ minutes$($round your response to two decimal$$ places$).$