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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-kx, for 0≤x<00 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 55 ft or less? P(0 ≤x≤ 55) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

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-kx, for 0≤x<00 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 55 ft or less? P(0 ≤x≤ 55) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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-kx, for 0≤x<00 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 55 ft or less? P(0 ≤x≤ 55) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)
Transcribed Image Text: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-kx, for 0≤x<00 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 55 ft or less? P(0 ≤x≤ 55) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)
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