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Exercise 3 (Application of Central Limit Theorems) (-) An airline decides to start an overbooking policy by accepting n > 200 reservations for flights operated by their 200-seats aircrafts. If more than 200 passengers show up for a flight, the first 200 are accepted whereas the remaining receive some kind of financial compensation. From historical data, it is estimated that the no-show probability for any passenger is 0.05 and that passengers can be considered independent. (a) Let S, be the random variable representing the number of passengers who show up for a 200-seats flight with n (possibly > 200) reservations. Give the distribution of Sn and express ES, and Var( S,) as functions of n. (b) The airline CEO would like to find the maximal value n such that P(S,.