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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 0sx< 00 A transportation planner determines that the average distance between cars on a certain highway is 90 ft. What is the probability that the distance between two successive cars, chosen at random, is 15 ft or less? P(0sxs 15) = (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 0sx< 00 A transportation planner determines that the average distance between cars on a certain highway is 90 ft. What is the probability that the distance between two successive cars, chosen at random, is 15 ft or less? P(0sxs 15) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.1: Continuous Probability Models
Problem 8E
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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< o0 A transportation planner determines that the average distance between cars on a certain highway is 90 ft. What is the probability that the distance between two successive cars, chosen at random, is 15 ft or less? P(0 <x< 15) = (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< o0 A transportation planner determines that the average distance between cars on a certain highway is 90 ft. What is the probability that the distance between two successive cars, chosen at random, is 15 ft or less? P(0 <x< 15) = (Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as needed.)
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