EBK BASIC BUSINESS STATISTICS
14th Edition
ISBN: 9780134685090
Author: STEPHAN
Publisher: VST
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Chapter 4, Problem 51PS
There are 15 exercise bikes in a fitness store showroom. The fitness store owner wishes to select three of them to display at a fitness expo. How many ways can a group three be selected?
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Students have asked these similar questions
4. Suppose that P(X = 1) = P(X = -1) = 1/2, that Y = U(-1, 1) and that X
and Y are independent.
(a) Show, by direct computation, that X + Y = U(-2, 2).
(b) Translate the result to a statement about characteristic functions.
(c) Which well-known trigonometric formula did you discover?
9. The concentration function of a random variable X is defined as
Qx(h) = sup P(x ≤ X ≤x+h), h>0.
x
(a) Show that Qx+b (h) = Qx(h).
(b) Is it true that Qx(ah) =aQx(h)?
(c) Show that, if X and Y are independent random variables, then
Qx+y (h) min{Qx(h). Qy (h)).
To put the concept in perspective, if X1, X2, X, are independent, identically
distributed random variables, and S₁ = Z=1Xk, then there exists an absolute
constant, A, such that
A
Qs, (h) ≤
√n
Some references: [79, 80, 162, 222], and [204], Sect. 1.5.
29
Suppose that a mound-shaped data set has a
must mean of 10 and standard deviation of 2.
a. About what percentage of the data should
lie between 6 and 12?
b. About what percentage of the data should
lie between 4 and 6?
c. About what percentage of the data should
lie below 4?
91002 175/1
3
Chapter 4 Solutions
EBK BASIC BUSINESS STATISTICS
Ch. 4 - Three coins are tossed. a. Give an example of a...Ch. 4 - An urn contain 12 red balls and 8 white balls. One...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - For each of the following, indicate whether the...Ch. 4 - For each of the following, state whether the...Ch. 4 - Which of the following events occur with a...Ch. 4 - Do Millennials or Gen-Xers feel more tense or...Ch. 4 - Referring to the contingency table in Problem 4.8,...Ch. 4 - How will markers change their social media use in...
Ch. 4 - Referring to the contingency table in Problem...Ch. 4 - Have the gains in student learning attributed to...Ch. 4 - Do Generation X and Boomers differ in how they use...Ch. 4 - A survey of 1,520 Americans, adults asked, “Do...Ch. 4 - Each year ratings are compiled concerning the...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - Consider the following contingency table: What is...Ch. 4 - If P(AandB)=0.4andP(B)=0.8,findP(AB).Ch. 4 - Prob. 19PSCh. 4 - ...Ch. 4 - Do Millennials or Gen-Xers feel more tense...Ch. 4 - How will marketers change their social media use...Ch. 4 - Do generation X and Boomers differ in how they use...Ch. 4 - Have the grains in student learning attributed to...Ch. 4 - A survey of 1,520 Americans adults asked “Do you...Ch. 4 - Each year, rating are compiled concerning the...Ch. 4 - In 42 of the 66 years from 1950 through 2010 (in...Ch. 4 - A standard deck of cards is being used to play a...Ch. 4 - A box of nine iPhone 7 cellphones contains two red...Ch. 4 - ...Ch. 4 - ...Ch. 4 - In Example 4.10 to suppose that the probability...Ch. 4 - Big Commerce launched a study to analyze modern...Ch. 4 - Olive Construction Company is determining whether...Ch. 4 - The 2016 Global Information Security Workforce...Ch. 4 - The editor of a textbook published company is...Ch. 4 - A municipal bond service has three rating...Ch. 4 - If there are 10 multiple-choice question on an...Ch. 4 - A lock on a bank vault consists of three dials,...Ch. 4 - a. If a coin is tossed seven times, how many...Ch. 4 - A particular brand of women’s jeans is available...Ch. 4 - Prob. 42PSCh. 4 - A team is being formed that includes four...Ch. 4 - In the National Basketball League there are five...Ch. 4 - Referring to Problem 4.44 how many different...Ch. 4 - A gardener has six rows available in his vegetable...Ch. 4 - How many different ways can a senior project...Ch. 4 - Four member of a group of 10 people are to be...Ch. 4 - A student has seven books that she would like to...Ch. 4 - A daily lottery is conducted in which 2 winning...Ch. 4 - There are 15 exercise bikes in a fitness store...Ch. 4 - What are the differences between a priori...Ch. 4 - What is the difference between a simple event and...Ch. 4 - How can you use the general addition rule to find...Ch. 4 - What is the difference between mutually exclusive...Ch. 4 - How does conditional probability relate to the...Ch. 4 - How does the multiplication rule differ for events...Ch. 4 - How can you use Bayes theorem in light of new...Ch. 4 - In Bayes’ theorem, how does the prior...Ch. 4 - What is the difference between Counting Rule 1 and...Ch. 4 - What is the difference between a permutation and...Ch. 4 - A survey by Accenture indicated that 64% of...Ch. 4 - Chartered Institute of personnel and Development...Ch. 4 - To better understand the website builder market,...Ch. 4 - Content Marketing institute provides insight on...Ch. 4 - The CMO survey collects and dissemination the...
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- 2,3, ample and rical t? the 28 Suppose that a mound-shaped data set has a mean of 10 and standard deviation of 2. a. About what percentage of the data should lie between 8 and 12? b. About what percentage of the data should lie above 10? c. About what percentage of the data should lie above 12?arrow_forward27 Suppose that you have a data set of 1, 2, 2, 3, 3, 3, 4, 4, 5, and you assume that this sample represents a population. The mean is 3 and g the standard deviation is 1.225.10 a. Explain why you can apply the empirical rule to this data set. b. Where would "most of the values" in the population fall, based on this data set?arrow_forward30 Explain how you can use the empirical rule to find out whether a data set is mound- shaped, using only the values of the data themselves (no histogram available).arrow_forward
- 5. Let X be a positive random variable with finite variance, and let A = (0, 1). Prove that P(X AEX) 2 (1-A)² (EX)² EX2arrow_forward6. Let, for p = (0, 1), and xe R. X be a random variable defined as follows: P(X=-x) = P(X = x)=p. P(X=0)= 1-2p. Show that there is equality in Chebyshev's inequality for X. This means that Chebyshev's inequality, in spite of being rather crude, cannot be improved without additional assumptions.arrow_forward4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward
- 8. Recall, from Sect. 2.16.4, the likelihood ratio statistic, Ln, which was defined as a product of independent, identically distributed random variables with mean 1 (under the so-called null hypothesis), and the, sometimes more convenient, log-likelihood, log L, which was a sum of independent, identically distributed random variables, which, however, do not have mean log 1 = 0. (a) Verify that the last claim is correct, by proving the more general statement, namely that, if Y is a non-negative random variable with finite mean, then E(log Y) log(EY). (b) Prove that, in fact, there is strict inequality: E(log Y) < log(EY), unless Y is degenerate. (c) Review the proof of Jensen's inequality, Theorem 5.1. Generalize with a glimpse on (b).arrow_forward3. Prove that, for any random variable X, the minimum of E(X - a)² is attained for a = EX. Provedarrow_forward7. Cantelli's inequality. Let X be a random variable with finite variance, o². (a) Prove that, for x ≥ 0, P(X EX2x)≤ 02 x² +0² 202 P(|X - EX2x)<≤ (b) Find X assuming two values where there is equality. (c) When is Cantelli's inequality better than Chebyshev's inequality? (d) Use Cantelli's inequality to show that med (X) - EX ≤ o√√3; recall, from Proposition 6.1, that an application of Chebyshev's inequality yields the bound o√√2. (e) Generalize Cantelli's inequality to moments of order r 1.arrow_forward
- The college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forwardThe Honolulu Advertiser stated that in Honolulu there was an average of 659 burglaries per 400,000 households in a given year. In the Kohola Drive neighborhood there are 321 homes. Let r be the number of homes that will be burglarized in a year. Use the formula for Poisson distribution. What is the value of p, the probability of success, to four decimal places?arrow_forwardThe college hiking club is having a fundraiser to buy new equipment for fall and winter outings. The club is selling Chinese fortune cookies at a price of $2 per cookie. Each cookie contains a piece of paper with a different number written on it. A random drawing will determine which number is the winner of a dinner for two at a local Chinese restaurant. The dinner is valued at $32. Since fortune cookies are donated to the club, we can ignore the cost of the cookies. The club sold 718 cookies before the drawing. Lisa bought 13 cookies. Lisa's expected earnings can be found by multiplying the value of the dinner by the probability that she will win. What are Lisa's expected earnings? Round your answer to the nearest cent.arrow_forward
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