Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poisson distribution. For simplicity, assume that there is only one lane and one worker who can serve at an average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three or more vehicles ahead of you?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Vehicles arrive at a car detailing service at a rate of 10 per minute according to a Poisson
distribution. For simplicity, assume that there is only one lane and one worker who can serve at
an average rate of 12 vehicles per minute. Service times are exponentially distributed.
Part A: What is the average length of the queue?
Part B: What is the average time a vehicle must spend to get through the system?
Part C: What is the utilization rate of the worker?
Part D: What is the probability that when you arrive at the shop, there will be three or
more vehicles ahead of you?
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