"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) =

0.15e−0.15(x − 0.5) x ≥ 0.5
0 otherwise
(a) What is the probability that time headway is at most 7 sec? (Round your answer to three decimal places.)

(b) What is the probability that time headway is more than 7 sec? At least 7 sec? (Round your answers to three decimal places.)
more than 7 sec
at least 7 sec

(c) What is the probability that time headway is between 6 and 7 sec? (Round your answer to three decimal places.)