A 24-hour fast food chain has defined the following sales strategy for its drive-thru service: "if you find more than three customers in the system (queue + service) you will receive a dessert for free". The cost of this policy is $ 2.00 per client who gets the free dessert. In the current condition, customers arrive randomly using a Poisson distribution at a rate of 18 per hour. Service is provided by just one employee and follows an exponential distribution with an average of 2.5 minutes. However, the manager estimates that through improvements in the order-fitting process, he will be able to reduce the average service time to 2.0 minutes. The graph attached shows the accumulated probability functions of having n customers in the drive-thru (queue + service) for two average service times (ST), in minutes. What is the probability of having more than four customers in the queue, for an average service time of 2 minutes?
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.
A 24-hour fast food chain has defined the following sales strategy for its drive-thru service: "if you find more than three customers in the system (queue + service) you will receive a dessert for free". The cost of this policy is $ 2.00 per client who gets the free dessert. In the current condition, customers arrive randomly using a Poisson distribution at a rate of 18 per hour. Service is provided by just one employee and follows an exponential distribution with an average of 2.5 minutes. However, the manager estimates that through improvements in the order-fitting process, he will be able to reduce the average service time to 2.0 minutes. The graph attached shows the accumulated
What is the probability of having more than four customers in the queue, for an average service time of 2 minutes?
Given that, the customers are arriving a t a rate of 18 per hour.
The service time is 2 minutes.
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