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:

Long-Acting Antipsychotic

A type of medication that is used to treat conditions like schizophrenia, with effects that last for an extended period, often administered through injections.

Medication Management

The process of overseeing the medications prescribed for a patient to ensure they are used appropriately.

Schizophrenia

A long-term mental disorder involving a breakdown in the relation between thought, emotion, and behavior, leading to faulty perception and withdrawal from reality.

Catatonia

A psychiatric condition marked by motor immobility or behavioral abnormality, such as stupor, rigidity, or extreme agitation.