The assumption of exponentially distributed service times indicates that
A)37% of the service times are less than the mean service time.
B)50% of the service times are less than the mean service time.
C)63% of the service times are less than the mean service time.
D)service time increase at an exponential rate as the waiting line grows.

Question

Quizplus · Accepted Answer

The cumulative distribution function of exponential distribution is given by F(x) = 1 - e^(-λx), where λ is the rate parameter. The mean of exponential distribution is 1/λ. Therefore, when the service times are exponentially distributed, we have P(X ≤ μ) = F(μ) = 1 - e^(-μ/μ) = 1 - e^(-1) ≈ 0.632, where μ is the mean service time. Therefore, approximately 63% of the service times are less than the mean service time.

The Assumption of Exponentially Distributed Service Times Indicates That