Question

Do you tailgate the car in front of you? About 30% of all drivers will tailgate before passing, thinking they can make the car in front of them go faster. Suppose that you are driving a considerable distance on a two-lane highway and are passed by 10 vehicles.

(b) Compute.. (check attachment)

Answer 1

The average time for another seven cars to pass after one car passes is 84 seconds.

Step-by-step explanation:

The question is asking us to compute the average time it takes for another seven cars to pass after one car passes. We are given that cars pass at an average rate of five cars per minute and that the duration of time between successive cars follows the exponential distribution. To solve this, we need to find the mean of the exponential distribution, which is equal to 1 divided by the rate parameter (in this case, 5). So the average time between successive cars is 1/5 minutes, or 12 seconds. To find the time it takes for another seven cars to pass, we simply multiply the average time between cars by seven. Therefore, the average time for another seven cars to pass is 7 times 12 seconds, which is 84 seconds.