The distance x, in feet, between successive cars on a certain stretch of highway

Question

The distance x, in feet, between successive cars on a certain stretch of highway has the following probability density function, where k 1/a and a is the average distance, in feet, between successive cars over some period of time f(x)-ke x, for 0sx00 A transportation planner determines that the average distance between cars on a certain highway is 140 ft. What is the probability that the distance between two successive cars, chosen at random, is 40 ft or less? oenween cars on acertain ig 140 t P(0 xs 40) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

Explanation / Answer

from above exponential distribution k=1/mean =1/140

therefore P(0<=x<=40 ) =1-e-kt =1-e-40/140 =0.2485

plese revert for any clarification required

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