United flight 15" has 182 seats. Because some people with reservations don't show up, United can overbook by accepting more than 182 reservations. Assume that there is a 0.0995 probability that a passenger with a reservation will not show up for the flight. Also assume that the airline accepts 200 reservations for the 182 seats that are available.
Find the probability that when 200 reservations are accepted, there are more passengers showing up than there are seats available. Is the probability of overbooking small enough so that it does no happen very often, or does it seem too high so that changes must be made to make it lower? Now use trial and error to find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05 or less.