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1. Airlines often oversell tickets. Suppose that a plane with 100 seats, 104 passengers have tickets. Let X be the number of ticketed passengers who actually show up for the flight. Assume that the probability mass function of X is given in the following table X 96 97 98 99 100 101 102 103 104 17 .06.05 p(x) .15 12 14 25 .04 .02 (a) Draw the probability histogram for the distribution of X. (b) What are the probabilities P(X ≤ 100) and P(98 < X < 102)? (c) If every passenger who does not get a seat needs to be compensated for $300, whereas every ticket was sold for $200. Let Z be the profit or loss of the airline due to overselling of 4 tickets, namely Z = 4*200 - (X-100)*300 if X> 100 and Z = 800 otherwise. What are the expected profit (EZ) and its associated standard deviation (SD(Z))? (Hint: As we have learnt in the class, a discrete random variable is completely specified by the value it takes and the associated probability vector. Try to find out what are the possible values of Z and the corresponding probabilities.)

1. Airlines often oversell tickets. Suppose that a plane with 100 seats, 104 passengers have tickets. Let X be the number of ticketed passengers who actually show up for the flight. Assume that the probability mass function of X is given in the following table X 96 97 98 99 100 101 102 103 104 17 .06.05 p(x) .15 12 14 25 .04 .02 (a) Draw the probability histogram for the distribution of X. (b) What are the probabilities P(X ≤ 100) and P(98 < X < 102)? (c) If every passenger who does not get a seat needs to be compensated for $300, whereas every ticket was sold for $200. Let Z be the profit or loss of the airline due to overselling of 4 tickets, namely Z = 4*200 - (X-100)*300 if X> 100 and Z = 800 otherwise. What are the expected profit (EZ) and its associated standard deviation (SD(Z))? (Hint: As we have learnt in the class, a discrete random variable is completely specified by the value it takes and the associated probability vector. Try to find out what are the possible values of Z and the corresponding probabilities.)

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 19PFA
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1. Airlines often oversell tickets. Suppose that a plane with 100 seats, 104 passengers have tickets. Let X be the number of ticketed passengers who actually show up for the flight. Assume that the probability mass function of X is given in the following table x p(x) 96 97 98 .15 .12 .14 99 100 101 102 103 104 25.17 06.05 .04 .02 (a) Draw the probability histogram for the distribution of X. (b) What are the probabilities P(X ≤ 100) and P(98 < X < 102)? (c) If every passenger who does not get a seat needs to be compensated for $300, whereas every ticket was sold for $200. Let Z be the profit or loss of the airline due to overselling of 4 tickets, namely Z = 4 * 200-(X-100)*300 if X > 100 and Z = 800 otherwise. What are the expected profit (EZ) and its associated standard deviation (SD(Z))? (Hint: As we have learnt in the class, a discrete random variable is completely specified by the value it takes and the associated probability vector. Try to find out what are the possible values of Z and the corresponding probabilities.)
Transcribed Image Text:1. Airlines often oversell tickets. Suppose that a plane with 100 seats, 104 passengers have tickets. Let X be the number of ticketed passengers who actually show up for the flight. Assume that the probability mass function of X is given in the following table x p(x) 96 97 98 .15 .12 .14 99 100 101 102 103 104 25.17 06.05 .04 .02 (a) Draw the probability histogram for the distribution of X. (b) What are the probabilities P(X ≤ 100) and P(98 < X < 102)? (c) If every passenger who does not get a seat needs to be compensated for $300, whereas every ticket was sold for $200. Let Z be the profit or loss of the airline due to overselling of 4 tickets, namely Z = 4 * 200-(X-100)*300 if X > 100 and Z = 800 otherwise. What are the expected profit (EZ) and its associated standard deviation (SD(Z))? (Hint: As we have learnt in the class, a discrete random variable is completely specified by the value it takes and the associated probability vector. Try to find out what are the possible values of Z and the corresponding probabilities.)
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