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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 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 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 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 b + c. W = 131a + 150b + 200c. Note that a, b, and c are independent of one another. a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W.

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 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 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 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 b + c. W = 131a + 150b + 200c. Note that a, b, and c are independent of one another. a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 7PPS
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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. a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) 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 on Sunday? g) What is the probability that X is within two standard deviations of its expected value? h) What is the probability that a is greater than b? i) What is the probability that a, b, and c are all less than their 50th percentiles?
Transcribed Image Text: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. a) Calculate the expected value of X. b) Calculate the standard deviation of X. c) Calculate the expected value of W. d) 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 on Sunday? g) What is the probability that X is within two standard deviations of its expected value? h) What is the probability that a is greater than b? i) What is the probability that a, b, and c are all less than their 50th percentiles?
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