United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some people with tickets don't show up, United will overbook by selling more than 180 tickets. If the flight is not overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some passengers are denied seats, the airline loses money from the compensation that must be given to bumped passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight. Also assume that airline sells 200 tickets for the 180 seats that are available.

1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight. Show your calculation (ie, what you put in the calculator) and round to 4 decimals.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight. Show your calculation (ie, what you put in the calculator) and round to 4 decimals.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight. Show your calculation (ie, what you put in the calculator) and round to 4 decimals.

4. Use trial and error to find the maximum number of tickets that could be sold so that the probability of "more passengers than seats" (ie, more than 180 passengers) is UNUSUAL.

Fill in the table below. (round all probabilities to 4 decimals)

Number of Reservations	P (more passengers than seats)
199
198
197
196
195
194
193
192
191

The maximum number of tickets that should be sold is ___________.