Elementary Statistics (13th Edition)
13th Edition
ISBN: 9780134464244
Author: Triola
Publisher: PEARSON
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Chapter 12, Problem 2RE
Author Readability Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer’s Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch Reading Ease scores for those pages are listed below. Do the authors appear to have the same level of readability?
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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 12 Solutions
Elementary Statistics (13th Edition)
Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 1-4, use the following listed arrival...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - In Exercises 5-16, use analysis of variance for...Ch. 12.1 - Prob. 10BSC
Ch. 12.1 - Triathlon Times Jeff Parent is a statistics...Ch. 12.1 - Arsenic in Rice Listed below are amounts of...Ch. 12.1 - Prob. 13BSCCh. 12.1 - Speed Dating Listed below are attribute ratings of...Ch. 12.1 - In Exercises 15 and 16, use the data set in...Ch. 12.1 - In Exercises 15 and 16, use the data set in...Ch. 12.1 - Tukey Test A display of the Bonferroni test...Ch. 12.2 - Two-Way ANOVA The pulse rates in Table 12-3 from...Ch. 12.2 - Two-Way ANOVA If we have a goal of using the data...Ch. 12.2 - Interaction a. What is an interaction between two...Ch. 12.2 - Balanced Design Does the table given in Exercise 1...Ch. 12.2 - Pulse Rates If we use the data given in Exercise 1...Ch. 12.2 - Weights The weights (kg) in the following table...Ch. 12.2 - Heights The heights (cm) in the following table...Ch. 12.2 - Pancake Experiment Listed below are ratings of...Ch. 12.2 - Marathon Times Listed below are New York City...Ch. 12.2 - Smoking, Gender, and Body Temperature The table...Ch. 12.2 - Transformations of Data Example 1 illustrated the...Ch. 12 - Cola Weights Data Set 26 Cola Weights and Volumes...Ch. 12 - Cola Weights For the four samples described in...Ch. 12 - Cola Weights For the analysis of variance test...Ch. 12 - Cola Weights Identify the value of the test...Ch. 12 - Cola Weights The displayed results from Exercise 1...Ch. 12 - One-Way ANOVA In general, what is one-way analysis...Ch. 12 - One vs. Two What is the fundamental difference...Ch. 12 - Estimating Length Given below is a Minitab display...Ch. 12 - Estimating Length Using the same results displayed...Ch. 12 - Estimating Length Using the same results displayed...Ch. 12 - Speed Dating Data Set 18 Speed Dating in Appendix...Ch. 12 - Author Readability Pages were randomly selected by...Ch. 12 - Prob. 3RECh. 12 - Speed Dating Listed below are attribute ratings of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 1-5, refer to the following list of...Ch. 12 - In Exercises 15, refer to the following list of...Ch. 12 - In Exercises 15, refer to the following list of...Ch. 12 - Quarters Assume that weights of quarters minted...Ch. 12 - Job Priority Survey USA Today reported on an...Ch. 12 - Win 4 Lottery Shown below is a histogram of digits...Ch. 12 - Does Weight Change with Age? Refer to Data Set 1...
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 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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