Question

if the average service rate is 6 customers per hour, and assuming the negative exponential distribution is used to describe the randomness of the service time distribution, what is the probability that the service time will be less than or equal to 6 minutes? a. 0.451 b. 0.549 c. 0.017 d. 0.632

Answer 1

Answer: If the service rate is 6 customers per hour, the mean service time can be calculated as 1/6 = 0.1 hours or 6 minutes. The negative exponential distribution is commonly used to model the service time distribution in queuing theory. The cumulative distribution function (CDF) of the negative exponential distribution is given by:

F(x) = 1 - e^(-λx)

where λ = 1/μ, where μ is the mean service time (in this case, μ = 0.1 hours or 6 minutes).

So, the probability that the service time will be less than or equal to 6 minutes can be calculated as:

F(6) = 1 - e^(-0.1 * 6) = 1 - e^(-0.6) ≈ 0.5488

So, the answer is approximately 0.549, which is closest to option (b).

Explanation: