A Crew of Mechanics at the Highway Department Garage Repair

question 41

Essay

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 10 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 12 vehicles per day with a repair time distribution that approximates a negative 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 6 or more vehicles in the system?

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Definitions:

Incompetent

Lacking the necessary skills, knowledge, or ability to do something successfully or as expected.

Funding

The act of providing financial resources, usually in the form of money, or other values such as effort or time, to finance a need, program, and project, usually by an organization or government.

Competitors' Products

Goods or services offered by rival businesses in the same industry, which vie for the same customer base or market share.

Business Incubator

An organization designed to help new and startup companies to develop by providing services such as management training or office space.