Toll booths on the New York State Thruway are often congested because of the large number of cars waiting to pay. A consultant working for the state concluded that if service times are measured from the time a car stops in line until it leaves, service times are exponentially distributed with a mean of 2.7 minutes. What proportion of cars can get through the toll booth in less than 3 minutes?

The proportion of cars can get through the toll booth in less than 3 minutes is 67%.

Step-by-step explanation:

Let the random variable X be defined as the service times at a tool booth.

The random variable X follows an Exponential distribution with parameter μ = 2.7 minutes.

The probability density function of X is:

Compute the probability that a car can get through the toll booth in less than 3 minutes as follows:

Thus, the proportion of cars can get through the toll booth in less than 3 minutes is 67%.