Through statistical analysis of historical data, Mile High Airlines has determined that the demand for one of its flights follows a Poisson distribution with a mean of 150 passengers. It has also determined that, out of the booked passengers, the number that actually show up for the flight follows a binomial distribution with a probability of success (i.e., probability of showing up) of 92 percent. The airline uses an Airbus 319 with 134 seats for this flight and has an overbooking limit of 13 passengers. That is, the airline policy is to overbook the flight by at most 13 passengers. If the flight is overbooked and more than 134 passengers show up for boarding, some passengers must be bumped to another flight. Bumping more than two passengers creates customer service problems for the airline in addition to the cost of compensating the bumped passengers. a. Create a Monte Carlo simulation to estimate the probability that more than two passengers are bumped with the current overbooking limit. Use at least 1000 simulation trials. b. What should the overbooking limit be if the airline would like to keep the probability of bumping more than two passengers to no more than 5 percent?
Through statistical analysis of historical data, Mile High Airlines has determined that the demand for one of its flights follows a Poisson distribution with a
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