Single order quantity inventory problem or Newsboy Problem:

A hotel near the university always fills up on the evening before football games. History has shown that when the hotel is fully booked, the number of last$-$minute cancellations has a mean of $5$ and standard deviation of $3.$ The average room rate is $$80.$ When the hotel is overbooked, the policy is to find a room in a nearby hotel and to pay for the room for the customer. This usually costs the hotel approximately $$200$ since rooms booked on such late notice are expensive. How many rooms should the hotel overbook $?$