An airline makes 200 reservations for a flight that holds 185 passengers. The probability that a passenger arrives for the flight is 0.9, and the passengers are assumed to be independent. (a) Approximate the probability that all the passengers who arrive can be seated. (b) Approximate the probability that the flight has empty seats. (c) Approximate the number of reservations that the airline should allow so that the probability that everyone who arrives can be seated is 0.95. [Hint: Successively try values for the number of reservations.]
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This can be modeled using a binomial distribution with parameters n = 200 (number of reservations) and p = 0.9 (probability that a passenger arrives). So, the probability mass function (PMF) is given by: P(X = k) = C(200, k) * (0.9)^k * (0.1)^(200-k) (a) Show more…
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