Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times.
-Use the information in Scenario B.6. What is the probability that there will be no tools in the system?
A) less than or equal to 0.16
B) greater than 0.16 but less than or equal to 0.19
C) greater than 0.19 but less than or equal to 0.22
D) greater than 0.22

Question

Quizplus · Accepted Answer

The probability of no tools in the system is given by the formula P0 = 1 / (1 + (λ / μ)), where λ is the arrival rate and μ is the service rate. In this case, λ = 1 / 30 and μ = 1 / 15, so P0 = 1 / (1 + (1 / 30) / (1 / 15)) = 0.1667.

Scenario B.6 The Jackson Machine Company Has Four Cutting Tools That Need