Average traffic spacing: The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is...

Average traffic spacing: The headway h is the average time between vehicles. On a highway carrying an average of 500 vehicles per hour, the probability P that the headway is at least t seconds is given45 by

a. What is the limiting value of P? Explain what this means in practical terms.

b. The headway h can be calculated as the quotient of the spacing f, in feet, which is the average distance between vehicles, and the average speed v, in feet per second, of traffic. Thus the probability that spacing is at least f feet is the same as the probability that the headway is at least f/v seconds. Use function composition to find a formula for the probability Q that the spacing is at least f feet. Note: Your formula will involve both f and v.

c. If the average speed is 88 feet per second (60 miles per hour), what is the probability that the spacing between two vehicles is at least 40 feet?