An airline is charged by an airport based upon the total taxi-time that an airplane spends to take off and land. Suppose taxi time, a, atairport A is normally distributed with mean of 27 minutes and standard deviation 8 minutes; taxi time, b, at airport B is normallydistributed with mean of 39 minutes and standard deviation 12 minutes; taxi time, c, at airport C is normally distributed with mean of 41minutes and standard deviation 10 minutes. JJ Airlines has a plane flying to airport A, airport B, and airport C on Sunday. Airport Acharges $131 per minute of taxi time; airport B charges $150 per minute of taxi time; airport c charges $200 per minute of taxi time. LetX = total amount of taxi time in minutes for the JJ plane. Let W = total taxi charges for the JJ plane. X is defined as X = a + b + c. W =131a + 150b + 200c. Note that a, b, and c are independent of one another.c) Calculate the expected value of W. 17587d) Calculate the standard deviation of W.e) If we pick a value k such that the probability that X > k equals .25 then calculate k?f) JJ Airlines has $20,000 available to pay for taxi time? What is the probability that JJ has enough to pay the total taxi time bill onSunday?Please solution USING R script

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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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An airline is charged by an airport based upon the total taxi-time that an airplane spends to take off and land. Suppose taxi time, a, at airport A is normally distributed with mean of 27 minutes and standard deviation 8 minutes; taxi time, b, at airport B is normally distributed with mean of 39 minutes and standard deviation 12 minutes; taxi time, c, at airport C is normally distributed with mean of 41 minutes and standard deviation 10 minutes. JJ Airlines has a plane flying to airport A, airport B, and airport C on Sunday. Airport A charges $131 per minute of taxi time; airport B charges $150 per minute of taxi time; airport c charges $200 per minute of taxi time. Let X = total amount of taxi time in minutes for the JJ plane. Let W = total taxi charges for the JJ plane. X is defined as X = a + b + c. W = 131a + 150b + 200c. Note that a, b, and c are independent of one another. d) Calculate the standard deviation of W. e) If we pick a value k such that the probability that X > k…
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