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 2 minutes for a particular customer to get a license renewal?
A)1
B)0.487
C)0.513
D)0

Question

Quizplus · Accepted Answer

The exponential distribution is given by the formula $P(X < x) = 1 - e^{-\lambda x}$, where $\lambda$ is the rate (1/3 per minute in this case) and $x$ is the time (2 minutes). Plugging in the values, we get $P(X < 2) = 1 - e^{-(1/3)(2)} = 1 - e^{-2/3} \approx 0.487$.

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