Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company’s office can be described by a Poisson probability distribution with an arrival rate of two jobs per 8-hour day. The time required to complete the jobs follows a normal distribution, with a mean time of 3.2 hours and a standard deviation of 2 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs: What is the mean arrival rate in jobs per hour? What is the mean service rate in jobs per hour? What is the average number of jobs waiting for service? What is the average time a job waits before the welder can begin working on it? What is the average number of hours between when a job is received and when it is completed? What percentage of the time is Gubser’s welder busy?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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  • Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company’s office can be described by a Poisson probability distribution with an arrival rate of two jobs per 8-hour day. The time required to complete the jobs follows a normal distribution, with a mean time of 3.2 hours and a standard deviation of 2 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs:
  1. What is the mean arrival rate in jobs per hour?
  2. What is the mean service rate in jobs per hour?
  3. What is the average number of jobs waiting for service?
  4. What is the average time a job waits before the welder can begin working on it?
  5. What is the average number of hours between when a job is received and when it is completed?
  6. What percentage of the time is Gubser’s welder busy?

 

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