I am having difficulty solving part e. Suppose that a popular hotel for vacation

Question

I am having difficulty solving part e.

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. 341 b. Given that the hotel books the number reservations ound in part a find the probability that at least 90% o the available rooms will be occupied on a given night. Round your answer to three decimal places 998 c. Given that the hotel books the number of reservations found in part a ind the probability that at most 80% of the available rooms will be occupied on a g en night. If your answer is zero, enter d. How does your answer to part a change as the required assurance rate increases from 95% to 97967 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%. Cancellation rate 10%

Explanation / Answer

e)

here let x is number of reservation done ; therefore mean numbr of arrival =x*(1-p)

where p is cancellation probability and std deviation =sqrt(x*p*(1-p))

also for 95% ; z score =1.645

therfore for P(X<301)=0.95

(301-x*(1-p))/sqrt(x*p*(1-p)) =1.645

solving abvoe:

rate reservation 5% 310 10% 324 15% 341 20% 360 25% 382

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