Statistics for Business & Economics, Revised (with XLSTAT Education Edition Printed Access Card)
13th Edition
ISBN: 9781337094160
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 2.2, Problem 24E
The DATAfile EngineeringSalary contains the
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3. Prove that, for any random variable X, the minimum of E(X - a)² is attained
for a = EX.
Proved
7. 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.
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.
Chapter 2 Solutions
Statistics for Business & Economics, Revised (with XLSTAT Education Edition Printed Access Card)
Ch. 2.1 - Methods 1. The response to a question has three...Ch. 2.1 - A partial relative frequency distribution is...Ch. 2.1 - A questionnaire provides 58 Yes, 42 No, and 20...Ch. 2.1 - for the 20102011 viewing season, the top five...Ch. 2.1 - In alphabetical order, the six most common last...Ch. 2.1 - Nielsen Media Research provided the list of the 25...Ch. 2.1 - The Canmark Research Center Airport Customer...Ch. 2.1 - Data for a sample of 55 members of the Baseball...Ch. 2.1 - Nearly 1.8 million bachelors degrees and over...Ch. 2.1 - VirtualTourist provides ratings for hotels...
Ch. 2.2 - Consider the following data. a. Develop a...Ch. 2.2 - Consider the following frequency distribution....Ch. 2.2 - Construct a histogram for the data in exercise 12.Ch. 2.2 - Consider the following data. a. Construct a dot...Ch. 2.2 - Construct a stem-and-leaf display for the...Ch. 2.2 - Construct a stem-and-leaf display for the...Ch. 2.2 - Applications A doctors office staff studied the...Ch. 2.2 - CBSSports.com developed the Total Player Ratings...Ch. 2.2 - Based on the tons handled in a year, the ports...Ch. 2.2 - The London School of Economics and the Harvard...Ch. 2.2 - Fortune provides a list of Americas largest...Ch. 2.2 - entrepreneur magazine ranks franchises using...Ch. 2.2 - The DATAfile EngineeringSalary contains the median...Ch. 2.2 - Each year America.EDU ranks the best paying...Ch. 2.2 - The 2011 Cincinnati Flying Pig Half-Marathon (13.1...Ch. 2.3 - The following data are for 30 observations...Ch. 2.3 - The following observations are for two...Ch. 2.3 - The Daytona 500 is a 500-mile automobile race held...Ch. 2.3 - The following crosstabulation shows the average...Ch. 2.3 - Recently, management at Oak Tree Golf Course...Ch. 2.3 - The following crosstabulation shows the number of...Ch. 2.3 - Each year Forbes ranks the worlds most valuable...Ch. 2.3 - Refer to Table 2.12. a. Prepare a crosstabulation...Ch. 2.3 - The U.S. Department of Energys Fuel Economy Guide...Ch. 2.4 - The following 20 observations are for two...Ch. 2.4 - Consider the following data on two categorical...Ch. 2.4 - The following crosstabulation summarizes the data...Ch. 2.4 - A study on driving speed (miles per hour) and fuel...Ch. 2.4 - The Current Results website lists the average...Ch. 2.4 - People often wait until middle age to worry about...Ch. 2.4 - Smartphones are advanced mobile phones with...Ch. 2.4 - The Northwest regional manager of an outdoor...Ch. 2 - Approximately 1.5 million high school students...Ch. 2 - The DATAfile MedianHousehold contains the median...Ch. 2 - Data showing the population by state in millions...Ch. 2 - A startup companys ability to gain funding is a...Ch. 2 - Consumer complaints are frequently reported to the...Ch. 2 - The term Beta refers to a measure of a stocks...Ch. 2 - The U.S. Census Bureau serves as the leading...Ch. 2 - western University has only one womens softball...Ch. 2 - Fortune magazine publishes an annual survey of the...Ch. 2 - Table 2.18 shows a portion of the data for a...Ch. 2 - Refer to the data set in Table 2.18. a. Construct...Ch. 2 - Refer to the data set in Table 2.18. a. Construct...Ch. 2 - Refer to the data set in Table 2.18. a. Prepare a...Ch. 2 - Google has changed its strategy with regard to how...Ch. 2 - A zoo has categorized its visitors into three...Ch. 2 - Pelican Stores Pelican Stores, a division of...Ch. 2 - Motion Picture Industry The motion picture...Ch. 2 - Queen City Cincinnati, Ohio, also known as the...
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- The 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_forwardWhat was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forward
- What was the age distribution of nurses in Great Britain at the time of Florence Nightingale? Thanks to Florence Nightingale and the British census of 1851, we have the following information (based on data from the classic text Notes on Nursing, by Florence Nightingale). Note: In 1851 there were 25,466 nurses in Great Britain. Furthermore, Nightingale made a strict distinction between nurses and domestic servants. Use a histogram and graph the probability distribution. Using the graph of the probability distribution determine the probability that a British nurse selected at random in 1851 would be 40 years of age or older. Round your answer to nearest thousandth. Age range (yr) 20–29 30–39 40–49 50–59 60–69 70–79 80+ Midpoint (x) 24.5 34.5 44.5 54.5 64.5 74.5 84.5 Percent of nurses 5.7% 9.7% 19.5% 29.2% 25.0% 9.1% 1.8%arrow_forwardThere are 4 radar stations and the probability of a single radar station detecting an enemy plane is 0.55. Make a histogram for the probability distribution.arrow_forwardshow all stepsarrow_forward
- Most people know that the probability of getting a head when you flip a fair coin is . You want to use the relative frequency of the event to show that the probability is . How many times should you simulate flipping the coin in the experiment? Would it be better to use 300 trials or 3000 trials? Explain.arrow_forwardThe qualified applicant pool for eight management trainee positions consists of ten women and six men. How many different groups of applicants can be selected for the positionsarrow_forwardYou want to make a salad from whatever vegetable you have in the fridge. You have seven different tomatoes. There are 2 red tomatoes, 4 yellow tomatoes, and one black tomato in the fridge. You have three different bell peppers. There is 1 red pepper, 1 yellow pepper, and 1 green pepper. What is the probability of randomly choosing a vegetable and getting a red tomato, and a green pepper? Round your answer to four decimal places.arrow_forward
- uppose automobile insurance companies gave annual premiums for top-rated companies in several states. The figure below shows box plots for the annual premium for urban customers in three states. Which state offers the lowest premium? Which state offers the highest premium?arrow_forwardWing Foot is a shoe franchise commonly found in shopping centers across the United States. Wing Foot knows that its stores will not show a profit unless they gross over $940,000 per year. Let A be the event that a new Wing Foot store grosses over $940,000 its first year. Let B be the event that a store grosses over $940,000 its second year. Wing Foot has an administrative policy of closing a new store if it does not show a profit in either of the first two years. Assume that the accounting office at Wing Foot provided the following information: 58% of all Wing Foot stores show a profit the first year; 72% of all Wing Foot store show a profit the second year (this includes stores that did not show a profit the first year); however, 86% of Wing Foot stores that showed a profit the first year also showed a profit the second year. Compute P(B|Ac). Round your answer to the nearest hundredth.arrow_forwardYou draw two cards from a standard deck of 52 cards, but before you draw the second card, you put the first one back and reshuffle the deck. If you get a3on the first card, find the probability of drawing a 3 for the second card.arrow_forward
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