Question 8: Use R to answer the following. Suppose that 30% of all students who have to buy a text for a particular course want a new copy (consider this 'success'), whereas the other 70% want a used copy. Consider randomly selecting 25 purchasers. (a) What are the mean value and standard deviation of the number who want a new copy of the book? (b) What is the probability that the number who want new copies is more than two standard deviations away from the mean value? (c) The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text, what is the probability that all 25 will get the type of book they want from current stock? [Hint: Let X = the number who want a new copy. For what values of X will all 25 get what they want?] (d) Suppose that new copies cost $100 and used copies cost $70. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 25 copies purchased? [Hint: Let h(X) = the revenue when X of the 25 purchasers want new copies. Express this as a linear function.]
Question 8: Use R to answer the following. Suppose that 30% of all students who have to buy a text for a particular course want a new copy (consider this 'success'), whereas the other 70% want a used copy. Consider randomly selecting 25 purchasers. (a) What are the mean value and standard deviation of the number who want a new copy of the book? (b) What is the probability that the number who want new copies is more than two standard deviations away from the mean value? (c) The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text, what is the probability that all 25 will get the type of book they want from current stock? [Hint: Let X = the number who want a new copy. For what values of X will all 25 get what they want?] (d) Suppose that new copies cost $100 and used copies cost $70. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 25 copies purchased? [Hint: Let h(X) = the revenue when X of the 25 purchasers want new copies. Express this as a linear function.]
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![Question 8:
Use R to answer the following. Suppose that 30% of all students who have to buy a text for
a particular course want a new copy (consider this 'success'), whereas the other 70% want a used copy. Consider randomly
selecting 25 purchasers.
(a) What are the mean value and standard deviation of the number who want a new copy of the book?
(b) What is the probability that the number who want new copies is more than two standard deviations away from the
mean value?
(c) The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text,
what is the probability that all 25 will get the type of book they want from current stock? [Hint: Let X = the number
who want a new copy. For what values of X will all 25 get what they want?]
(d) Suppose that new copies cost $100 and used copies cost $70. Assume the bookstore currently has 50 new copies and
50 used copies. What is the expected value of total revenue from the sale of the next 25 copies purchased? [Hint: Let
h(X) = the revenue when X of the 25 purchasers want new copies. Express this as a linear function.]
Question 9:
Use R to answer the following. Let X have a binomial distribution with parameters n = 25 and
p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation
(with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation.
(a) P(15 ≤X ≤ 20)
(b) P(X ≤ 15)
(c) P(20 < X)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5d0f5588-edbf-4bb6-ac13-d0c35130e4e5%2Fd07d3cb2-9733-4ad9-ad5b-61b56b7d994f%2Fg4gilkd_processed.png&w=3840&q=75)
Transcribed Image Text:Question 8:
Use R to answer the following. Suppose that 30% of all students who have to buy a text for
a particular course want a new copy (consider this 'success'), whereas the other 70% want a used copy. Consider randomly
selecting 25 purchasers.
(a) What are the mean value and standard deviation of the number who want a new copy of the book?
(b) What is the probability that the number who want new copies is more than two standard deviations away from the
mean value?
(c) The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text,
what is the probability that all 25 will get the type of book they want from current stock? [Hint: Let X = the number
who want a new copy. For what values of X will all 25 get what they want?]
(d) Suppose that new copies cost $100 and used copies cost $70. Assume the bookstore currently has 50 new copies and
50 used copies. What is the expected value of total revenue from the sale of the next 25 copies purchased? [Hint: Let
h(X) = the revenue when X of the 25 purchasers want new copies. Express this as a linear function.]
Question 9:
Use R to answer the following. Let X have a binomial distribution with parameters n = 25 and
p=0.6. Calculate each of the following probabilities using both the binomial distribution and the normal approximation
(with the continuity correction). Make sure to check that this an an appropriate use of the normal approximation.
(a) P(15 ≤X ≤ 20)
(b) P(X ≤ 15)
(c) P(20 < X)
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