Problem 2 (20 Points, 5 each)
The plane for a certain flight has 19 seats available for passengers. Past data shows that 90% of the customers of this flight actually show up, the remaining 10% do not show up. In order to maximize the revenues, the airline sells 20 tickets for this flight. Supposing all passengers behave independently, answer the following questions.
Hint: Use the binomial distribution and the cumulative binomial table.
a. What is the expected number of passengers showing up for the flight?
b. What is the probability that the number of passengers showing up is the same as the number of seats? (In other words, all passengers have a seat and there are no empty seats.)