2. [Airline industries] Each airplane has capacity for 200 passengers, and overbooking is a common practice in these industries. (a) [10 points] To sell more tickets than available seats, the airline needs to estimate the probability that each passenger will attend the flight. Suppose that each passenger will attend the flight with probability p. The airline uses ~ as the estimate of p, where n is the number of sold tickets and X is the number of people who attended the flight. How large n should be to estimate p within 0.1 with confidence of 0.99? (b) [20 points] According to the historical data, each passenger will attend a flight with probability Pattend = 0.9. What is the maximum number of tickets the airline can sell to ensure that no one is left behind with probability 0.75? (Hint: Use Chebychev's inequality, roots of 0.9r- +0.6x -200 = 0 are -15.24 and 14.58)