The Department of Motor Vehicles DMV can service customers a

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?

Solution

Here, the cumulative distribution for this exponential distribution, as the mean time is 60min/20 = 3 min is

F(x) = 1 - exp((-1/3)x)

Thus,

P(x<2) = F(2) = 1 - exp((-1/3)*2) = 0.486582881 [ANSWER]