Question

Cars arrive at a toll booth according to a Poisson process with mean 60 cars per hour. If the attendant makes a three minute phone call, what is the probability that the number of cars passing through the toll booth during the call is between 2 and 4, inclusive?

Answer 1

Suppose, random variable X denotes number of cars arrive during the phone call of 3 minutes.

Clearly, number of cars arrival follows Poisson distribution.

Expected number of cars to arrive in 3 minutes E(X) = 60*3/60 = 3

We know,

So, required probability is given by

Hence, probability that number of cars passing through the toll booth during the call is between 2 and 4 is 0.616115.