Reference no: EM13635380

Suppose that a popular hotel for vacationers in Orlando, Florida, has a total room of 300 identical rooms. As many major airline companies do, this hotel has a total adopted an overbooking policy in an effort to maximaze 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 reservation found in part a, find the propability 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 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% (increments of 5%)? Assume now that the required assurance rate remains at 95%?