A Local Bank Has Two Drive-Through Teller Windows with an Essentially

question 13

Essay

A local bank has two drive-through teller windows with an essentially unlimited queue length. They estimate that the arrival rate during their most busy time will average about 40 cars per hour. They also estimate they can serve an average of 50 cars per hour. Management wants to make sure that the system is operating efficiently.
a. What is the probability that there will be no cars in the system?
b. On average, how many cars are in the system?
c. How long would a car be waiting (in seconds) in the drive-through, on average?

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Definitions:

Expected Value

The predicted value of a variable, calculated as a sum of all possible values each multiplied by the probability of its occurrence.

Insurance Policy

A contractual agreement between an individual or entity and an insurance company, outlining the terms for the insurer to compensate the insured for specific losses in exchange for premiums paid.

Premium

An amount paid in addition to a standard price, often for insurance, or a higher or more privileged level of service or product.

Expected Value

A calculated average of all possible outcomes of a particular random variable, weighted by their respective probabilities.