Problem 15-27 (Algorithmic) 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 three jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 1.9 hours and a standard deviation of 1 hour. Answer the following questions, assuming that Gubser uses one welder to complete all jobs: What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places. ________________per Hour What is the mean service rate in jobs per hour? If required, round your answer to four decimal places. ________________per hour What is the average number of jobs waiting for service? If required, round your answer to three decimal places. ______________________ What is the average time a job waits before the welder can begin working on it? If required, round your answer to one decimal place. _________________hours What is the average number of hours between when a job is received and when it is completed? If required, round your answer to one decimal place. ___________________hours What percentage of the time is Gubser's welder busy? __________________% of the time the welder is busy.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Problem 15-27 (Algorithmic)
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 three jobs per 8-hour day. The time required to complete the jobs follows a
- What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places.
________________per Hour - What is the mean service rate in jobs per hour? If required, round your answer to four decimal places.
________________per hour - What is the average number of jobs waiting for service? If required, round your answer to three decimal places.
______________________ - What is the average time a job waits before the welder can begin working on it? If required, round your answer to one decimal place.
_________________hours - What is the average number of hours between when a job is received and when it is completed? If required, round your answer to one decimal place.
___________________hours - What percentage of the time is Gubser's welder busy? __________________% of the time the welder is busy.
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