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 between 2 and 3 minutes to be served?
A)0.4831
B)0
C)1
D)0.1419

Question

Quizplus · Accepted Answer

The rate of service is 1/3 per minute. So, the parameter λ of exponential distribution is λ=1/3. 
Let X be the time it takes to renew the license. Then X follows an exponential distribution with parameter λ=1/3. 
Using the cumulative distribution function (CDF) of exponential distribution, we can find the probability as follows:
P(2<X<3)=F(3)-F(2)=e^(-λ*2)-e^(-λ*3)
= e^(-1/3*2) - e^(-1/3*3)
= 0.3910 - 0.2491
= 0.1419 
Therefore, the probability that it will take between 2 and 3 minutes to be served is 0.1419. 
The best choice is D.

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