Condé Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List (Condé Nast Traveler, January 2004). Suppose Broadmoor's marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30.
a. What is the probability all the hotel's rooms will be rented?
b. What is the probability 50 or more rooms will not be rented?
c. Would you recommend the hotel consider offering a promotion to increase demand? What considerations would be important?