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Tpy6a [65]
4 years ago
14

Suppose that a popular hotel for vacationers in Orlando, Florida, has a total of 300 identical rooms. As many major airline comp

anies 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. 270 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. (Round your answer to three decimal places.) 270 c. Given that the hotel books the number of reservations found in part a, find the probability that at most 80% of the available rooms will be occupied on a given night. (If your answer is zero, enter "0".) d. How does your answer to part a change as the required assurance rate increases from 95% to 97%

Mathematics
1 answer:
Alona [7]4 years ago
7 0

Answer:

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 of reservations found in part a, find the probability that at least 90% of the available rooms will be occupied on a given night. = 0.0072

c. Given that the hotel books the number of reservations found in part a, find the probability that at most 80% of the available rooms will be occupied on a given night. = 0.1157

d. How does your answer to part a change as the required assurance rate increases from 95% to 97% = 338.8

Step-by-step explanation:

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Answer:

Claire traveled for 9 days.

Step-by-step explanation:

Given:

Total Distance traveled = 701 miles

Distance traveled each day = 80 miles

Distance traveled on last day = 61 miles

We need to find the number of days Claire traveled.

Solution:

Let the number of days Claire traveled be denoted by 'd'.

Now we can say that;

Total Distance traveled is equal to sum of Distance traveled each day multiplied by number of days and Distance traveled on last day.

framing in equation form we get;

80d+61=701

Now Subtracting both side by 61 using Subtraction Property of Equality we get;

80d+61-61=701-61\\\\80d = 640

Now Dividing both side by 80 we get;

\frac{80d}{80}=\frac{640}{80}\\\\d=8

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Step-by-step explanation:

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