A company has three claims representatives who have 8 hour working days, Monday to Friday. Clients come to the offices of the company at a rate of 20 clients per 8 hour day. The time a representative spends to each customer obeys an exponential law with an average service time of 36 minutes. In taking the hour as a unit of time, answer the following questions: (a) How many hours per week is a representative busy on average? (b) What is the average time spent by a customer in the queue before being served by a representative? (c) What is the average number of representatives who are unoccupied? (d) What is the probability that there is a queue?

A company has three claims representatives who have 8 hour working days, Monday to Friday. Clients come to the offices of the company at a rate of 20 clients per 8 hour day. The time a representative spends to each customer obeys an exponential law with an average service time of 36 minutes. In taking the hour as a unit of time, answer the following questions: (a) How many hours per week is a representative busy on average? (b) What is the average time spent by a customer in the queue before being served by a representative? (c) What is the average number of representatives who are unoccupied? (d) What is the probability that there is a queue?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

(a)

How many hours per week is a representative busy on average?

(b)

What is the average time spent by a customer in the queue before being served by a representative?

(c)

What is the average number of representatives who are unoccupied?

(d)

What is the probability that there is a queue?

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Step 1: Calculate Average time a representative is busy per week

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Step 2: Calculate Average Waiting Time

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Step 3: Calculate average number of representatives

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Step 4: Calculate probability that there is a queue

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