On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed. a. On average, how long does it take before a job is completed (measured from the time the job arrives at the factory)? b. What fraction of the time is the factory idle? c. What is the probability that work on a job will begin within two days of its arrival at the factory?

On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed. a. On average, how long does it take before a job is completed (measured from the time the job arrives at the factory)? b. What fraction of the time is the factory idle? c. What is the probability that work on a job will begin within two days of its arrival at the factory?

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

On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distributed. The factory can process an average of 42 jobs per day, and the time to process a job is exponentially distributed.
a. On average, how long does it take before a job is completed (measured from the time the job arrives at the factory)?
b. What fraction of the time is the factory idle?
c. What is the probability that work on a job will begin within two days of its arrival at the factory?

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