### An airline''s goal is to fill the plane as much as possible

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On any given flight, an airline's goal is to fill the plane as much as possible without overbooking. If, on average, 10% of customers cancel their tickets, all independently of each other, what is the probability that a particular flight will be overbooked if the airline sells 320 tickets for a plane that has a maximum capacity of 300 people? What is the probability that a plane with maximum capacity 150 people will be overbooked if the airline sells 160 tickets? Express the answers in terms of the standard normal cumulative distribution function, Φ(x). (Hint. Consider the probability p of a success to be the probability that a given person actually shows up for the flight. From this, deduce what the effective mean and standard deviation are for the number of successes in the case when n = 320 or when n = 160, respectively.)

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