Star Airlines serves the route between Washington, DC (National), and Portsmouth, NH, with a single flight daily. The airline sells both discount-fare and full-fare tickets. The airline has assigned a 150-seat aircraft to the flight. Using Littlewoods rule, the airline has determined that the optimal booking limit for a flight departing in two weeks is 50. The full fare for this flight is $300 and the discount fare is $100. And the mean of the full-fare demand is estimated at 80. The standard deviation of the full-fare demand for this flight is ___ (rounding to integer!), assuming that the full-fare demand follows a normal distribution.

The Inn at Penn hotel has 150 rooms with standard queen-size beds and two rates: a full price of $300 and a discount price of $120. To receive the discount price, a customer must purchase the room at least two weeks in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Tuesday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel with a normal distribution with a mean 1000 and a standard deviation of 100. Historically, the hotel estimates that the demand from business travelers is distributed normally with a mean of 70 rooms and a standard deviation of 29. Find the optimal booking limit _____ for discount rooms.