A Crew of Mechanics at the Highway Department Garage Repair

question 4

Essay

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution.
(a) What is the utilization rate for this service system?
(b) What is the average time before the facility can return a breakdown to service?
(c) How much of that time is spent waiting for service?
(d) How many vehicles are likely to be waiting for service at any one time?

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Definitions:

Scatterplot

A graph that uses dots to represent values obtained for two different variables, showing the relationship between them.

Correlation

A statistical measure that indicates the extent to which two or more variables fluctuate together.

Regression

In statistics, the act of estimating the relationship between variables, allowing for the prediction of one variable based on the value of another.

Residuals

The differences between observed values and the values predicted by a model, indicating the discrepancy in data fit.