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 five jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 1.3 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? Round your answer to four decimal places.
jobs per hour
What is the mean service rate in jobs per hour? Round your answer to four decimal places.
jobs per hour
What is the average number of jobs waiting for service? Round your answer to three decimal places.

What is the average time a job waits before the welder can begin working on it? 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? Round your answer to one decimal place.
hours
What percentage of the time is Gubser's welder busy? Round your answer to the nearest whole number.
% of the time the welder is busy.

a) Mean arrival rate in jobs per hour = 0.6250

b) Mean service rate in jobs per hour = 0.7692

c) The average number of jobs waiting for service = 2.802

d) Average time a job waits before the welder can begin working on it = 4.5 hours

e) Average number of hours between when a job is received and when it is completed = 5.8 hours

f) Percentage of the time is Gubser's welder busy = 81%

Explanation:

As given,

Number of jobs = 5

Rate = 8 hour per day

Average hours = 1.3

Standard deviation - 1 hour

a)

Mean arrival =

                    = = 0.6250 per hour

⇒Mean arrival rate in jobs per hour = 0.6250

b)

Mean service rate =

                              = = 0.7692 per hour

⇒Mean service rate in jobs per hour = 0.7692

c)

Average number of job waiting for service =

                                                                       = = 2.802

⇒The average number of jobs waiting for service = 2.802

d)

Average time a job waits before the welder can begin working on it =

                                                                                                                  = 4.5 hr

⇒Average time a job waits before the welder can begin working on it = 4.5 hours

e)

Average number of hours between when a job is received and when it is completed = 4.5 +

                 = 4.5 + 1.3

                 = 5.8 hours

⇒Average number of hours between when a job is received and when it is completed = 5.8 hours

f)

Percentage of the time is Gubser's welder busy = ×100%

                                                                                = 0.8125×100%

                                                                                = 81.25% ≈ 81%

⇒Percentage of the time is Gubser's welder busy = 81%

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