There are 300 hotel rooms at a hotel. 15% chance of cancellation for each room. What is the max # of rooms you can book with a 95% chance that you won't be overbooked.

Printable View

- Jul 26th 2006, 02:47 PMmagicpuntHotel Rooms probability
There are 300 hotel rooms at a hotel. 15% chance of cancellation for each room. What is the max # of rooms you can book with a 95% chance that you won't be overbooked.

- Jul 26th 2006, 03:24 PMThePerfectHacker
That do not make no sense to me.

Repeat question, from the way I understand it, the answer is impossible. - Jul 26th 2006, 05:14 PMmagicpunt
p(a reservation will be kept) = .85 and those who don't keep their reservation simply don't show up, thus taking up a room without paying for it

- Jul 26th 2006, 05:28 PMThePerfectHackerQuote:

Originally Posted by**magicpunt**

*at least one*is .95 or more. If you have what is the probability that you do not get a room? Well, each one is .15 and there are thus the probability is OF GETTING AT LEAST ONE ROOM, is

and you want that . Thus,

Thus,

Thus,

Make chart, for values,

Note at we have already it less than .05

However, I am sure if this is what you mean. - Jul 26th 2006, 07:02 PMmagicpunt
I appreciate the help but let me rephrase.

You are the hotel manager. You have 300 hotel rooms in your hotel. There is an 85% chance that those who book a room will actually show up and a 15% chance that they will not (thus the room is "booked" but not used).

You want to book as many rooms as possible so that there is a 95% chance that all of those who book with you will have a room (a 95% confidence that you won't be overbooked). - Jul 27th 2006, 01:27 AMCaptainBlackQuote:

Originally Posted by**magicpunt**

Then the question is:

What is the largest M such that

P=P(0|M)+P(1|M) + P(2|M) + .. + P(300|M)>=0.95 ?

(that is: what is the maximum number of bookings M so that there is less

than a 5% chance of more than 300 shows?).

RonL - Jul 27th 2006, 01:33 AMJakeDQuote:

Originally Posted by**magicpunt**

Treat the number of rooms taken as a normal variable with mean and standard deviation Find the maximum with the probability Can you take it from here? - Jul 27th 2006, 03:07 AMCaptainBlackQuote:

Originally Posted by**JakeD**

RonL - Jul 27th 2006, 03:11 AMCaptainBlackQuote:

Originally Posted by**JakeD**

Standard deviation of a binomial RV with probability of

success on single trial and trials is:

RonL - Jul 27th 2006, 08:18 AMJakeDQuote:

Originally Posted by**CaptainBlack**

As for the continuity correction, there ain't no stinking continuity correction in the Central Limit Theorem! ;) - Jul 27th 2006, 10:06 AMCaptainBlackQuote:

Originally Posted by**JakeD**

B(721, 0.232, 10342) - the probability of 721 success in 10342 trials

each with a probability of a favourable outcome of 0.232? :)

RonL