Wayne's service center operates a welding shop. Assume that the arrival of jobs follows a Poisson distribution with 2 jobs arriving in an 8 hour day. The time required to complete a job follows a normal distribution with a mean time of 3.2 hours and a standard deviation of 2 hours. A. What is the mean service rate in jobs per hour?
B. What is the average number of jobs waiting for service?
C. What is the average time a job waits before the welder can begin working on it?
D. What is the average number of hours between when a job is received and when it is completed?
E. What percentage of the time is Gubser's welder busy?

a) 0.3125 per hour

b) 2.225 hours

c) 8.9 hours

d) 12.1 hours

e) 80%

Step-by-step explanation:

Given that:

mean time = 3.2 hours, standard deviation (σ) = 2 hours

The  mean service rate in jobs per hour (λ) = 2 jobs/ 8 hour = 0.25 job/hour

a) The average number of jobs waiting for service (μ)= 1/ mean time = 1/ 3.2 = 0.3125 per hour

b) The average time a job waits before the welder can begin working on it (L) is given by:

c) The average number of hours between when a job is received and when it is completed (Wq) is given as:

d) The average number of hours between when a job is received and when it is completed (W) is given as:

e) Percentage of the time is Gubser's welder busy (P) is given as:

9514 1404 393

  x = 4

Step-by-step explanation:

I like to put these in the form f(x) = 0. We can do that by subtracting the right side. Common factors can be cancelled from numerator and denominator, provided they are not zero.

_____

If you leave the numerator as (x-3)(4-x), then there are two values of x that make it zero. Because x=3 makes the equation "undefined", it cannot be considered to be a solution.