A Crew of Mechanics at the Highway Department Garage Repair

question 45

Essay

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 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:

Rainfall

The amount of precipitation, in the form of liquid water drops, that falls to the ground from clouds.

Corals

Marine invertebrates in the class Anthozoa that often live in compact colonies; they are major contributors to the physical structure of coral reefs.

Symbiotic

Symbiotic refers to a mutually beneficial relationship between two different organisms living in close physical association.

Bleaching

The process of removing color from a substance, often through chemical means, which can also refer to the destruction of coral coloration due to environmental stress like warm sea temperatures.