Problem 3 (Reserving Capacity): You manage a hotel with 200 rooms in Arlington, Texas. The NCAA Championship Game is coming up. Sports fans either book a room in advance or wait until the last minute. Those who book in advance pay a bargain rate ($200/night) and those who book late pay a premium rate ($500/night). Suppose you can easily get 200 advance reservations, and fill up your hotel. Number of last minute customers is Normally distributed with mean 75 and standard deviation 25. How many rooms should be set aside for last-minute customers?