If service time follows an exponential probability distribution,approximately 63% of the service times are less than the mean service time.

Question

Quizplus · Accepted Answer

This is a property of the exponential distribution. The cumulative distribution function for an exponential distribution is given by P(X ≤ t) = 1 - e^(-λt), where λ is the rate parameter. The mean service time is equal to 1/λ. Therefore, P(X ≤ mean service time) = P(X ≤ 1/λ) = 1 - e^(-λ/λ) = 1 - e^(-1) ≈ 0.63212, which is approximately 63%.

If Service Time Follows an Exponential Probability Distribution,approximately 63% of the Service