Answered: Gubser Welding, Inc., operates a…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 64E

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Question

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 probability distribution, with a mean time of 2.7 hours and a standard deviation of 1.9 hours. Answer the following questions, assuming that Gubser uses one welder to complete all jobs.

(a)

What is the mean arrival rate in jobs per hour? (Round your answer to four decimal places.)

per hour

(b)

What is the mean service rate in jobs per hour? (Round your answer to four decimal places.)

per hour

(c)

What is the average number of jobs waiting for service? (Round your answer to four decimal places.)

(d)

What is the average time (in hours) a job waits before the welder can begin working on it? (Round your answer to two decimal places.)

(e)

What is the average number of hours between when a job is received and when it is completed? (Round your answer to two decimal places.)

(f)

What percentage of the time is Gubser's welder busy? (Round your answer to the nearest whole number.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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