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 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? 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.

Average number of job = (Mean arrival rate^2 × Standard deviation^2 + (mean arrival rate ÷ mean service rate)^2) ÷ 2(1 - (mean arrival rate ÷ mean service rate)^2)

= (0.25^2 × 2^2 + (0.25 ÷ 0.3125)^2) ÷ 2(1-(0.25 ÷ 0.3125))

= 0.25 + 1.60

= 1.85

Average time taken by job waiting = Average number of job waiting ÷ Mean arrival rate

= 1.85 ÷ 0.25

= 7.4 hours

Average number of hours a job received and completed = Average time taken by job waiting + 1 ÷ Mean service rate

= 7.4 + 1 ÷ 0.3125

= 10.6 hours

Gubser's welder busy percentage of time = Mean arrival rate ÷ Mean service rate

= 0.25 ÷ 0.3125

= 0.80

= 80%