Math Problem Statement
Question content area top
Part 1
Suppose that the probability that a passenger will miss a flight is
0.09570.0957.
Airlines do not like flights with empty seats, but it is also not desirable to have overbooked flights because passengers must be "bumped" from the flight. Suppose that an airplane has a seating capacity of
5555
passengers.
(a) If
5757
tickets are sold, what is the probability that
5656
or
5757
passengers show up for the flight resulting in an overbooked flight?
(b) Suppose that
6161
tickets are sold. What is the probability that a passenger will have to be "bumped"?
(c) For a plane with seating capacity of
290290
passengers, what is the largest number of tickets that can be sold to keep the probability of a passenger being "bumped" below
11%?
Question content area bottom
Part 1
(a) The probability of an overbooked flight is
0.02270.0227.
(Round to four decimal places as needed.)
Part 2
(b) The probability that a passenger will have to be bumped is
enter your response here.
(Round to four decimal places as needed.)
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial Distribution
Normal Approximation
Formulas
Mean: μ = np
Standard Deviation: σ = √(npq)
Z-score: Z = (X - μ) / σ
Normal Approximation to Binomial Distribution
Theorems
Central Limit Theorem
Continuity Correction
Suitable Grade Level
College/University Level (Statistics/Probability)
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