The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time: Is no more than 3 minutes?
A).3012
B).6988
C).4346
D).5654
E).0821

Question

Quizplus · Accepted Answer

We know that the mean service time, μ = 2.5 minutes. We can use the formula for the cumulative distribution function (cdf) of an exponential distribution, which is:

F(x) = 1 - e^(-λx)

where λ is the rate parameter, which is equal to 1/μ for exponential distributions. So, λ = 1/2.5 = 0.4.

To find the probability that the service time is no more than 3 minutes, we want to calculate:

P(X ≤ 3) = F(3) = 1 - e^(-0.4*3) ≈ 0.6988

Therefore, the best choice is B, with a probability of approximately 0.6988.

The Cashier Service Time at the Local Branch of the Rivertown