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Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 10 students per hour, and the average service rate is 20 students per hour. A student has just entered the system. How long is she expected to stay in the system (in minutes)?

Respuesta :

The amount of time that she is expected to stay in the system is; 7.5 Minutes

How to find the average of Exponential Functions?

We are given;

The average number of arrivals of customers, λ = 12 students/hour.

The average service rate of a single server; μ = 20 students/hour.

The average of an exponential distribution is given by the formula:

E(X) = 1/μ

However, the amount of time that she is expected to stay in the system is;

t = 1/(μ - λ)

t = 1/(20 - 12)

t = 0.125 hours

Converting to minutes gives;

t = 0.125 * 60

t = 7.5 minutes

Read more about Average of Exponential Functions at; https://brainly.com/question/16095228

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