Sam the Vet Is Running a Rabies Vaccination Clinic for Dogs

question 120

Essay

Sam the Vet is running a rabies vaccination clinic for dogs at the local grade school.Sam 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 1 dog every 4 minutes, according to a Poisson distribution.Also assume that Sam's vaccinating times are exponentially distributed.
(a)Find the probability that Sam is idle.
(b)Find the proportion of time that Sam is busy.
(c)Find the average number of dogs receiving or waiting to be vaccinated.
(d)Find the average number of dogs waiting to be vaccinated.
(e)Find the average time a dog waits before getting vaccinated.
(f)Find the average amount (mean)of time a dog spends between waiting in line and getting vaccinated.

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Definitions:

Industrial Nations

Countries that are highly developed and have a major portion of their economy based on manufacturing and industry.

Labor Productivity

A measure of economic performance that compares the amount of goods and services produced (output) with the number of hours worked to produce those goods and services.

Economies Of Scale

Cost advantages that enterprises obtain due to their scale of operation, resulting in decreased costs per unit.

Technological Advance

Improvements in technology, leading to more efficient production processes, new product features, or entirely new products.