A university department maintains an emergency computer repair shop. History shows that broken computers arrive for repair randomly, but with average rates that depend on the number of computers that are already in the shop. The average arrival rates are shown below: no. computers already in the shop 0 1 2 3 4 average arrival rate (no. per day) 5 4 4 3 0 The technician in the shop can repair computers at an average rate of 4 computers per day. However, whenever there are 3 or more computers in the shop for repair, an extra technician is used, and this doubles the average rate of computer repair to 8 computers per day. a) What is the probability that an extra technician is used? b) What is the expected number of computers in the shop awaiting service? c) The policy of using the extra technician was introduced because the shop wishes to return computers to users within a half-day of the computers arrival in the shop, on average. What is the average amount of time that a computer is in the shop? Does the shop achieve its goal of returning computers to the users in a half-day or less?
A university department maintains an emergency computer repair shop. History shows that broken computers arrive for repair randomly, but with average rates that depend on the number of computers that are already in the shop. The average arrival rates are shown below: no. computers already in the shop 0 1 2 3 4 average arrival rate (no. per day) 5 4 4 3 0 The technician in the shop can repair computers at an average rate of 4 computers per day. However, whenever there are 3 or more computers in the shop for repair, an extra technician is used, and this doubles the average rate of computer repair to 8 computers per day. a) What is the probability that an extra technician is used? b) What is the expected number of computers in the shop awaiting service? c) The policy of using the extra technician was introduced because the shop wishes to return computers to users within a half-day of the computers arrival in the shop, on average. What is the average amount of time that a computer is in the shop? Does the shop achieve its goal of returning computers to the users in a half-day or less?
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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Transcribed Image Text:A university department maintains an emergency
computer repair shop. History shows that broken
computers arrive for repair randomly, but with
average rates that depend on the number of
computers that are already in the shop. The average
arrival rates are shown below:
no. computers already in the shop
average arrival rate (no. per day)
1
2
3
4
4
4
3
The technician in the shop can repair computers at
an average rate of 4 computers per day. However,
whenever there are 3 or more computers in the
shop for repair, an extra technician is used, and this
doubles the average rate of computer repair to 8
computers per day.
a) What is the probability that an extra technician is
used?
b) What is the expected number of computers in the
shop awaiting service?
c) The policy of using the extra technician was
introduced because the shop wishes to return
computers to users within a half-day of the
computers arrival in the shop, on average. What is
the average amount of time that a computer is in
the shop? Does the shop achieve its goal of
returning computers to the users in a half-day or
less?
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