Question

In the past, there were toll stations in Taiwan’s highways, but toll stations often cause traffic jams because there are a lot of cars waiting to pay. A government-hired expert defines the service time from a car parking line until leaving, the service time is in accordance with the exponential distribution, of the average value is 2.6 minutes. What is the probability of passing the toll booth in less than 3 minutes? (round off to the 3rd decimal place)

Answer 1

Say X be the service time from a car parking line until leaving.

The variable X follows an exponential distribution, having λ = 1 / 2.6

We need to find the probability of a car passing the toll booth in less than 3 minutes. The formula is:

This is the formula of the cumulative exponential distribution.

To find: F(3) = 1 - e^-3/2.6 = 1 - e^-1.154 = 1 - 0.315 = 0.685