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 3 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.

a) The probability that Tarun is idle = . 4 (round your response to two decimal places).
b) The proportion of the time that Tarun is busy = . 6 (round your response to two decimal places).
c) The average number of dogs being vaccinated and waiting to be vaccinated = 1.5 dogs (round your response to two decimal places).
d) The average number of dogs waiting to be vaccinated = . 9 dogs (round your response to two decimal places).
e) The average time a dog waits before getting vaccinated = nothing minutes (round your response to two decimal places).

a) Probability that Tarun is idle = 0.4

b) Proportion of the time that Tarun is busy = 0.6

c) The average number of dogs being vaccinated and waiting to be vaccinated = 1.5 dogs

d) The average number of dogs waiting to be vaccinated = 0.9 dogs

e) The average time a dog waits before getting vaccinated = 0.075 mins = 4.5 hrs

Step-by-step explanation:

a) Let the probability that Tarun is idle = P

Probability that Tarun is not idle = P₀

P + P₀ = 1

Average number of dogs shot in 1 hr(60 mins),   = 20 dogs/hr

Rate of dog arrival, = 12 dogs/hr

Probability that Tarun is idle, P = 1 - P₀

P = 0.4

b) Proportion of the time that Tarun is busy(not idle):

c) The average number of drugs being vaccinated and waiting to be vaccinated.

n = 1.5 dogs

d) The average number of drugs waiting to be vaccinated:

n = 0.9 dogs

e) The average time a dog waits before getting vaccinated:

Waiting time = 0.075 minutes

Waiting time = 0.075 * 60

Waiting time = 4.50 hrs

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1