Answer:
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 = ![\frac{No. of jobs}{rate}](https://tex.z-dn.net/?f=%5Cfrac%7BNo.%20of%20jobs%7D%7Brate%7D)
=
= 0.6250 per hour
⇒Mean arrival rate in jobs per hour = 0.6250
b)
Mean service rate = ![\frac{hour}{average hour}](https://tex.z-dn.net/?f=%5Cfrac%7Bhour%7D%7Baverage%20hour%7D)
=
= 0.7692 per hour
⇒Mean service rate in jobs per hour = 0.7692
c)
Average number of job waiting for service = ![\frac{(0.6250)^{2} (1)^{2} + \frac{0.6250}{0.7692} }{2 ( 1 - \frac{0.6250}{0.7692} )}](https://tex.z-dn.net/?f=%5Cfrac%7B%280.6250%29%5E%7B2%7D%20%281%29%5E%7B2%7D%20%2B%20%5Cfrac%7B0.6250%7D%7B0.7692%7D%20%7D%7B2%20%28%201%20-%20%5Cfrac%7B0.6250%7D%7B0.7692%7D%20%29%7D)
=
= 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 = ![\frac{2.802}{0.6250}](https://tex.z-dn.net/?f=%5Cfrac%7B2.802%7D%7B0.6250%7D)
= 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%