Time headway in traffic flow is the elapsed time between the

\"Time headway\" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow. The pdf of X is the following.

f(x) =

(a) What is the probability that time headway is at most 5 sec? (Round your answer to three decimal places.)


(b) What is the probability that time headway is more than 5 sec? At least 5 sec? (Round your answers to three decimal places.)

(c) What is the probability that time headway is between 4 and 5 sec? (Round your answer to three decimal places.)

Solution