Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. As many major airline companies do, this hotel has adopted an overbooking policy in an effort to maximize the usage of its available lodging capacity. Assume that each potential hotel customer holding a room reservation, independently of other customers, cancels the reservation or simply does not show up at the hotel on a given night with probability 0.15.
a. Find the largest number of room reservations that this hotel can book and still be at least 95% sure that everyone who shows up at the hotel will have a room on a given night.
b. Given that the hotel books the number of reservations found in part a, find the probability that at least 90% of the available rooms will be occupied on a given night.
c. Given that the hotel books the number of reservations found in part a, find the probability that at most 80% of the available rooms will be occupied on a given night.
d. How does your answer to part a change as the required assurance rate increases from 95% to 97%? How does your answer to part a change as the required assurance rate increases from 95% to 99%?
e. How does your answer to part a change as the cancellation rate varies between 5% and 25% (in increments of 5%)? Assume now that the required assurance rate remains at 95%.