What percentage of the time is the postal clerk busy

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Reference no: EM132312318

1. Sam Certo, a Nanaimo vet, is running a rabies vaccination clinic for dogs at the local grade school. Sam can "shoot" a dog every three minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every six minutes according to a Poisson distribution. Also assume that Sam's shooting times are exponentially distributed. Compute the following:

a) The probability that Sam is idle.

b) The proportion of the time that Sam is busy.

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

d) The average number of dogs waiting to be vaccinated.

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

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

2. Automobiles arrive at the drive-through window at the downtown Fort McMurray post office at the rate of four every 10 minutes. The average service time is two minutes. The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

a) What is the average time a car is in the system?

b) What is the average number of cars in the system?

c) What is the average number of cars waiting to receive service?

d) What is the average time a car is in the queue?

e) What is the probability that there are no cars at the window?

f) What percentage of the time is the postal clerk busy?

g) What is the probability that there are exactly two cars in the system?

h) By how much would your answer to part (a) be reduced if a second drive-through window, with its own server, were added?

Reference no: EM132312318

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