A Crew of Mechanics at the Highway Department Garage Repair

question 69

Essay

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 5 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a.What is the probability that the system is empty?
b.What is the probability that there is precisely one vehicle in the system?
c.What is the probability that there is more than one vehicle in the system?
d.What is the probability of 5 or more vehicles in the system?

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Definitions:

Principal Place of Business

The primary location where a business's executive and management activities are conducted or where its central administration is based.

Business

An organized effort by individuals to produce and sell, for a profit, the goods and services that satisfy society's needs.

Settled

Resolved or finalized, especially in the context of legal disputes or agreements.

Motor Vehicle Accident

An incident involving a collision or other mishap involving vehicles such as cars, motorcycles, or trucks, often resulting in damage or injury.