Essentials of Statistics, Books a la Carte Edition (5th Edition)
5th Edition
ISBN: 9780321926739
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 3.3, Problem 44BSC
Chebyshev's Theorem Based on Data Set 3 in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a
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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?
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3
2,3,
ample
and
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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?
27 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?
Chapter 3 Solutions
Essentials of Statistics, Books a la Carte Edition (5th Edition)
Ch. 3.2 - Employment Data listed below are results from the...Ch. 3.2 - Average The web site IncomeTaxList.com lists the...Ch. 3.2 - Median In an editorial, the Poughkeepsie Journal...Ch. 3.2 - Prob. 4BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 8BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 10BSC
Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 14BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - Prob. 18BSCCh. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 5-20, find the (a) mean, (b) median,...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - Prob. 23BSCCh. 3.2 - In Exercises 21-24, find the mean and median for...Ch. 3.2 - Large Data Sots from Appendix B. In Exercises...Ch. 3.2 - Prob. 26BSCCh. 3.2 - Prob. 27BSCCh. 3.2 - Prob. 28BSCCh. 3.2 - Prob. 29BSCCh. 3.2 - In Exercises 29-32, find the mean of the data...Ch. 3.2 - Prob. 31BSCCh. 3.2 - In Exercises 29-32, find the mean of the data...Ch. 3.2 - Degrees of Freedom Carbon monoxide is measured in...Ch. 3.2 - Prob. 34BBCh. 3.2 - Trimmed Mean Because the mean is very sensitive to...Ch. 3.2 - Prob. 36BBCh. 3.2 - Prob. 37BBCh. 3.2 - Quadratic Mean The quadratic mean (or root mean...Ch. 3.2 - Prob. 39BBCh. 3.3 - Comparing Variation Which do you think has less...Ch. 3.3 - Correct Statements? Which of the following...Ch. 3.3 - Variation and Variance In statistics, how do the...Ch. 3.3 - Prob. 4BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 7BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 9BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 11BSCCh. 3.3 - Prob. 12BSCCh. 3.3 - Prob. 13BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 15BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 18BSCCh. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - In Exercises 5-20, find the range, variance, and...Ch. 3.3 - Prob. 21BSCCh. 3.3 - Prob. 22BSCCh. 3.3 - Prob. 23BSCCh. 3.3 - Prob. 24BSCCh. 3.3 - Prob. 25BSCCh. 3.3 - Prob. 26BSCCh. 3.3 - Prob. 27BSCCh. 3.3 - Prob. 28BSCCh. 3.3 - Prob. 29BSCCh. 3.3 - Estimating Standard Deviation with the Range Rule...Ch. 3.3 - Prob. 31BSCCh. 3.3 - Prob. 32BSCCh. 3.3 - Prob. 33BSCCh. 3.3 - Prob. 34BSCCh. 3.3 - Identifying Unusual Values with the Range Rule of...Ch. 3.3 - Prob. 36BSCCh. 3.3 - Prob. 37BSCCh. 3.3 - Finding Standard Deviation from a Frequency...Ch. 3.3 - Prob. 39BSCCh. 3.3 - Finding Standard Deviation from a Frequency...Ch. 3.3 - Prob. 41BSCCh. 3.3 - The Empirical Rule Based on Data Set 3 Body...Ch. 3.3 - Prob. 43BSCCh. 3.3 - Chebyshev's Theorem Based on Data Set 3 in...Ch. 3.3 - Why Divide by n 1? Let a population consist of...Ch. 3.3 - Prob. 46BBCh. 3.4 - z Scores James Madison, the fourth President of...Ch. 3.4 - Prob. 2BSCCh. 3.4 - Prob. 3BSCCh. 3.4 - Prob. 4BSCCh. 3.4 - Prob. 5BSCCh. 3.4 - Prob. 6BSCCh. 3.4 - Prob. 7BSCCh. 3.4 - Prob. 8BSCCh. 3.4 - Prob. 9BSCCh. 3.4 - Prob. 10BSCCh. 3.4 - Usual and Unusual Values.In Exercises 9-12,...Ch. 3.4 - Usual and Unusual Values.In Exercises 9-12,...Ch. 3.4 - Prob. 13BSCCh. 3.4 - Prob. 14BSCCh. 3.4 - Comparing Values.In Exercises 13-16, use z scores...Ch. 3.4 - Prob. 16BSCCh. 3.4 - Percentiles. In Exercises 17-20, use the following...Ch. 3.4 - Prob. 18BSCCh. 3.4 - Prob. 19BSCCh. 3.4 - Prob. 20BSCCh. 3.4 - Prob. 21BSCCh. 3.4 - Prob. 22BSCCh. 3.4 - Prob. 23BSCCh. 3.4 - Prob. 24BSCCh. 3.4 - Prob. 25BSCCh. 3.4 - Prob. 26BSCCh. 3.4 - Prob. 27BSCCh. 3.4 - Prob. 28BSCCh. 3.4 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.4 - Prob. 30BSCCh. 3.4 - Prob. 31BSCCh. 3.4 - Boxplots. In Exercises 29-32, use the given data...Ch. 3.4 - Prob. 33BSCCh. 3.4 - Boxplots from Larger Data Sets In Appendix B. In...Ch. 3.4 - Prob. 35BSCCh. 3.4 - Boxplots from Larger Data Sets In Appendix B. In...Ch. 3.4 - Prob. 37BBCh. 3.4 - Prob. 38BBCh. 3 - Find the mean of these times that American...Ch. 3 - What is the median of the sample values listed in...Ch. 3 - Prob. 3CQQCh. 3 - The standard deviation of the sample values in...Ch. 3 - The taxi-in times for 48 flights that landed in...Ch. 3 - You plan to investigate the variation of taxi-in...Ch. 3 - Consider a sample taken from the population of all...Ch. 3 - Consider a sample taken from the population of all...Ch. 3 - Approximately what percentage of taxi-in times is...Ch. 3 - Prob. 10CQQCh. 3 - Ergonomics When designing an eye-recognition...Ch. 3 - z Score Using the sample data from Exercise 1,...Ch. 3 - Boxplot Using the same standing heights listed in...Ch. 3 - Prob. 4RECh. 3 - Prob. 5RECh. 3 - Aircraft Design Engineers designing overhead bin...Ch. 3 - Prob. 9RECh. 3 - Moan or Median? A statistics class with 40...Ch. 3 - Designing Gloves An engineer is designing a...Ch. 3 - Frequency Distribution Use the hand lengths in...Ch. 3 - Histogram Use the frequency distribution from...Ch. 3 - Stemplot Use the hand lengths from Exercise 1 to...Ch. 3 - Descriptive Statistics Use the hand lengths in...Ch. 3 - Normal Distribution Instead of using the hand...Ch. 3 - Sampling Shortly after the World Trade Center...Ch. 3 - Prob. 8CRE
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- 30 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_forward5. 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_forward
- 4. Prove that, for any random variable X, the minimum of EIX-al is attained for a = med (X).arrow_forward8. 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_forward
- 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.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_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_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_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_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
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