Allegiant Airlines is considering an overbooking policy for one of its flights. The airplane has 50 seats, but Allegiant is considering accepting more reservations than seats because sometimes passengers do not show up for their flights, resulting in empty seats. ThePassengerAppearanceworksheet in the fileOverbookingcontains data on 1,000 passengers showing whether or not they showed up for their respective flights.

Click on the datafile logo to reference the data.

In addition, Allegiant has conducted a field experiment to gauge the demand for reservations for the current flight. During this experiment, they did not limit the number of reservations for the flight to observe the uncensored demand. The following table summarizes the result of the field experiment.

No. of Reservations DemandedProbability480.05490.05500.15510.30520.25530.10540.10Allegiant receives a marginal profit of $100 for each passenger who books a reservation (regardless of whether they show up). Allegiant incurs a rebooking cost of $300 for each passenger who books a reservation, but is denied seating due to a full airplane; this cost results from rescheduling the passenger and any loss of goodwill.

To control its rebooking costs, Allegiant wants to set a limit on the number of reservations it will accept. Evaluate Allegiant's average net profit for reservation limits of 50, 52, and 54, respectively.

Round your answers to a whole dollar amount.

Reservation LimitAverage Net Profit50$52$54$Based on the 95% confidence intervals for average net profit, which reservation limit do you recommend? Round your answers to a whole dollar amount.

We are 95% confident that Allegiant Airlines can achieve a net profit between $and $by limiting the number of reservations to-