A Crew of Mechanics at the Highway Department Garage Repair

question 56

Essay

A crew of mechanics at the Highway Department garage repair vehicles which 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:

Hierarchical Ladder

A system of organization where individuals or entities are ranked one above the other according to status or authority.

Big Three

A term that can refer to the three dominant entities in any given industry or sector, often implying their power and influence over market dynamics.

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The capacity or ability an individual possesses that may indicate their likelihood of becoming an effective leader.

Omnipotent Authority

An individual or entity possessing complete power and influence, often seen within religious or mythological contexts.