A hotel near St. Thomas always fills up on the evening before football games. Historical data tells us that when the hotel is fully booked, the number of last minute cancellations has a mean of 6 and a standard deviation of 4. The average room rate $100. When the hotel is overbooked, the policy is to find a room in a nearby hotel and pay the room for the customer. This usually costs the hotel on average $200 since rooms booked on such late notice are very expensive.
How many rooms should the hotel overbook?
For the hotel to be 90% sure that they do not have a single room unoccupied, how many rooms should the hotel overbook?