What is the probability that a machine will have to wait for service with two operators?
A).654
B).090
C).346
D).910
E).016

Question

Quizplus · Accepted Answer

The probability that a machine will have to wait for service with two operators can be found using the formula P(Wait) = ρ^2/(1-ρ), where ρ is the utilization rate of each operator. Assuming that the service times are exponentially distributed and the arrival rate is constant, we can use the formula ρ = λ/μ, where λ is the arrival rate and μ is the service rate of each operator. Since there are two operators, the total service rate is 2μ. Without any information given, we can assume that the arrival rate is equal to the service rate, i.e., λ = μ. Hence, ρ = λ/μ = 1, which gives P(Wait) = 1/3 = 0.346. Therefore, the best choice is C.

What Is the Probability That a Machine Will Have to Wait