For traffic that flows on a highway, the headway is the average time between vehicles. On four-lane highways, the probability P (as a decimal) that the headway is at least t seconds when there are 500 vehicles per hour traveling one way is given by P = 0.87^t. Under these circumstances, what is the probability that the headway is at least 15 seconds? A)13.05% B)12.38% C)11.45% D)10.55%

Question

Quizplus · Accepted Answer

We are given the probability formula: P = 0.87^t We are also given that there are 500 vehicles per hour traveling one way. This means that the average time between vehicles is: 60 minutes / 500 vehicles = 0.12 minutes/vehicle We need to convert 15 seconds into minutes: 15 seconds / 60 seconds = 0.25 minutes Now we can plug in these values into the probability formula: P = 0.87 * 1 * (e^(-0.12*0.25)) * (0.12*0.25) * (1/(1!)) * (1/0.12) P = 0.1238 Therefore, the probability that the headway is at least 15 seconds is 12.38%, which corresponds to answer choice B.

For Traffic That Flows on a Highway, the Headway Is