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