The Department of Motor Vehicles (DMV)can service customers at a rate of 20 per hour (or 1/3 per minute)when it comes to license renewals.The service time follows an exponential distribution.What is the probability that it will take less than 3 minutes for a particular customer to get a license renewal?
A)0.5
B)0
C)1
D)0.368

Question

Quizplus · Accepted Answer

We know that the DMV can service customers at a rate of 1/3 per minute. This means that the service time can be modeled by the exponential distribution with parameter lambda = 1/3.

To find the probability that a particular customer will get a license renewal in less than 3 minutes, we need to calculate the cumulative distribution function (CDF) of the exponential distribution as follows:

P(X < 3) = 1 - e^(-lambda*3) = 1 - e^(-1) ≈ 0.632

Therefore, the probability that it will take less than 3 minutes for a particular customer to get a license renewal is about 0.632, which corresponds to choice D.

The Department of Motor Vehicles (DMV)can Service Customers at a Rate