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 (sec). suppose that in a particular traffic environment, the distribution of time headway has the following form.

f(x) = k/(x^7) ; x > 1

0 ; x< 1

(a) determine the value of k for which f(x) is a legitimate pdf.
(b) what is the probability that headway is within 1 standard deviation of the mean value?