Sam the Vet Is Running a Rabies Vaccination Clinic for Dogs

question 89

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 6 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:

Basil I

Byzantine Emperor from 867 to 886 AD, founder of the Macedonian dynasty, known for his administrative reforms and military campaigns.

Hagia Sophia

A historic architectural marvel in Istanbul, originally an Eastern Orthodox cathedral, later an Ottoman mosque, and now a museum.

San Vitale

An early Christian church in Ravenna, Italy, famed for its stunning Byzantine mosaics, dating back to the 6th century.

Mosaic Program

An initiative or project that involves assembling small pieces of colored glass, stone, or other materials to create a picture or pattern.