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# Hotel Overbooking - Binomial Distribution

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 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) Using 322 reservations, find the probability that at least 90% of the available rooms will be occupied on a given night. [322 rooms x .90 = 289.80]

(c) Using 322 reservations, find the probability that at least 85% of the available rooms will be occupied on a given night. [322 rooms x .85 = 273.70]

#### Solution Preview

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 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 ...

#### Solution Summary

Probability is calculated using Binomial distribution.

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