Let X represent the time it takes from when someone enters the line for a roller coaster until they exit on the other side. Consider the probability model defined by the cumulative distribution function given below.     0   x < 3 F(x) = (x-3)/1.18   3 < x < 4.18     1   x > 4.18 a) What is E(x)? Give answer to three decimal places. b) What is the value c such that P(X <= c) = 0.28? Give your answer to four decimal places. c) What is the probability that X falls within 0.31 minutes of its mean? Give your answer to four decimal places.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section: Chapter Questions
Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...
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Let X represent the time it takes from when someone enters the line for a roller coaster until they exit on the other side. Consider the probability model defined by the cumulative distribution function given below.



    0   x < 3
F(x) = (x-3)/1.18   3 < x < 4.18
    1   x > 4.18

a) What is E(x)? Give answer to three decimal places.

b) What is the value c such that P(X <= c) = 0.28? Give your answer to four decimal places.

c) What is the probability that X falls within 0.31 minutes of its mean? Give your answer to four decimal places.

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