Math Problem Statement
Because many passengers who make reservations do not show up, airlines often overbook flights (sell more tickets than there are seats). A certain airplane holds 164 passengers. If the airline believes the rate of passenger no-shows is 9% and sells 176 tickets, is it likely they will not have enough seats and someone will get bumped? Bold a right parenthesis font size decreased by 1 Use the normal model to approximate the binomial to determine the probability of at least 165 passengers showing up. Bold b right parenthesis font size decreased by 1 Should the airline change the number of tickets they sell for this flight? Explain. Question content area bottom Part 1 Bold a right parenthesis font size decreased by 1 The probability of at least 165 passengers showing up is 0.127. (Round to three decimal places as needed.) Part 2 b) Should the airline change the number of tickets they sell for this flight? Explain. A. The probability is fairly low, so it is likely that they should not change the number of tickets they sell. However, the decision also depends on the relative costs of not selling seats and bumping passengers. B. Since the probability is so low, they should not change the number of tickets they sell. C. Since the probability is so high, they should change the number of tickets they sell. D. The probability is fairly high, so it is likely that they should sell less. However, the decision also depends on the relative costs of not selling seats and bumping passengers.
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Normal Approximation
Formulas
Mean: μ = n * p
Standard Deviation: σ = sqrt(n * p * (1 - p))
Z-score: Z = (X - μ) / σ
Theorems
Normal Approximation to Binomial Theorem
Continuity Correction
Suitable Grade Level
Grades 10-12
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