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Because not all airline passengers show up for their reserved seat, an airline sells 129 tickets for a flight that holds only 123 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. Round your answers to two decimal places (e.g 98.76) (a) What is the probability that every passenger who shows up gets a seat? (b) What is the probability that the flight departs with empty seats? (c) What are the mean and (d) standard deviation of the number of passengers who show up?

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Answer #1

Let the random variable X denote the number of passengers with tickets who do not show
up. (X=number of passengers that don’t show up out of 129.)
There are 0,1,2,3,… ,n=129 possible passengers
The probability that a passenger does not show is 0.1 (10% do not show),
or p = 0.1
Notice we have a binomial distribution with parameters p = 0.1 and n = 129
X~Bin(n = 129, p = 0.1)
が , 189 121-m、 ב1 - o.oo87 o 91 2 3.4)

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