Suppose that a popular hotel for vacationers in Orlando Flor

Suppose that a popular hotel for vacationers, in Orlando, Florida has
a total of 300 identical rooms. Like many major airline companies,
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 the probability of 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 any given night

b. Given that the hotel books the number of reservations found in
answering 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
answering part a, find the probability that at most 90% 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 you 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 is held fixed at 95%.

Solution