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Part $1$

Dr$.$ Tarun$$ Gupta, a Michigan$$ vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can$$ "shoot" a dog $4$ every minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every $5$ minutes according to a Poisson distribution. Also assume that$$ Tarun's shooting times are negative exponentially distributed.

Part $2$

$$a$)$ The probability that Tarun is idle$=$

$$

$.20($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ The proportion of the time that Tarun is busy$=$

$$

$.79($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ The average number of dogs being vaccinated and waiting to be vaccinated$=$

$($round your response to two decimal$$ places$)$