Assume that a hospitality company operates a hotel with 107 rooms on a particular day. Historically, the probability that a customer will show up for a randomly selected reservation is 97%. 1. Assume that all 107 rooms were booked. Let X be the number of reservations for which the customer showed up. a. Describe the distribution of X: X~? (n = = p= b. Find the probability that there will be available rooms at the end of the day, in other words, find the probability that not all customers will show up: P(X ≤ (Round the answer to 4 decimal places) c. Find the expected number of customers who show up for their room reservations: E[X] = [ (Round the answer to the whole number) d. Find the expected number of available rooms at the end of the day by subtracting the E[X] from the number of available rooms: (Round the answer to the whole number) 2. Assume that the hospitality company sells 2 more booking(s). Let Y be the number of reservations for which the customer showed up. a. Describe the distribution of Y: Y~? (n: く = p = b. Find the probability that more customers will show up than there are available rooms: P(Y> (Round the answer to 4 decimal places)
Assume that a hospitality company operates a hotel with 107 rooms on a particular day. Historically, the probability that a customer will show up for a randomly selected reservation is 97%. 1. Assume that all 107 rooms were booked. Let X be the number of reservations for which the customer showed up. a. Describe the distribution of X: X~? (n = = p= b. Find the probability that there will be available rooms at the end of the day, in other words, find the probability that not all customers will show up: P(X ≤ (Round the answer to 4 decimal places) c. Find the expected number of customers who show up for their room reservations: E[X] = [ (Round the answer to the whole number) d. Find the expected number of available rooms at the end of the day by subtracting the E[X] from the number of available rooms: (Round the answer to the whole number) 2. Assume that the hospitality company sells 2 more booking(s). Let Y be the number of reservations for which the customer showed up. a. Describe the distribution of Y: Y~? (n: く = p = b. Find the probability that more customers will show up than there are available rooms: P(Y> (Round the answer to 4 decimal places)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
Related questions
Question
![Assume that a hospitality company operates a hotel with 107 rooms on a particular day. Historically, the
probability that a customer will show up for a randomly selected reservation is 97%.
1. Assume that all 107 rooms were booked. Let X be the number of reservations for which the customer
showed up.
a. Describe the distribution of X:
X~? (n =
=
p=
b. Find the probability that there will be available rooms at the end of the day, in other words, find
the probability that not all customers will show up:
P(X ≤
(Round the answer to 4 decimal places)
c. Find the expected number of customers who show up for their room reservations:
E[X] =
[
(Round the answer to the whole number)
d. Find the expected number of available rooms at the end of the day by subtracting the E[X] from
the number of available rooms:
(Round the answer to the whole number)
2. Assume that the hospitality company sells 2 more booking(s). Let Y be the number of reservations for
which the customer showed up.
a. Describe the distribution of Y:
Y~? (n:
く
=
p =
b. Find the probability that more customers will show up than there are available rooms:
P(Y>
(Round the answer to 4 decimal places)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F218414e4-3b46-4b83-912e-0cd4fb336a27%2Fa724518d-e758-4679-b6c3-49a7219a33bd%2Fcvtqqwx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Assume that a hospitality company operates a hotel with 107 rooms on a particular day. Historically, the
probability that a customer will show up for a randomly selected reservation is 97%.
1. Assume that all 107 rooms were booked. Let X be the number of reservations for which the customer
showed up.
a. Describe the distribution of X:
X~? (n =
=
p=
b. Find the probability that there will be available rooms at the end of the day, in other words, find
the probability that not all customers will show up:
P(X ≤
(Round the answer to 4 decimal places)
c. Find the expected number of customers who show up for their room reservations:
E[X] =
[
(Round the answer to the whole number)
d. Find the expected number of available rooms at the end of the day by subtracting the E[X] from
the number of available rooms:
(Round the answer to the whole number)
2. Assume that the hospitality company sells 2 more booking(s). Let Y be the number of reservations for
which the customer showed up.
a. Describe the distribution of Y:
Y~? (n:
く
=
p =
b. Find the probability that more customers will show up than there are available rooms:
P(Y>
(Round the answer to 4 decimal places)
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