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Mathematical Interest Theory 3rd Edition Leslie Jane, James Daniel, Federer Vaaler - Solutions

Based on results from a Bradley Corporation poll, assume that 70% of adults always wash their hands after using a public restroom. a. Find the probability that among 8 randomly selected adults, exactly 5 always wash their hands after using a public restroom. b. Find the probability that among 8
Find the probability that a female has a back-to-knee length between 22.0 in. and 24.0 in. Use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including
Find the probability that a male has a back-to-knee length between 22.0 in. and 24.0 in. Use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including
Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) ≤ 0.01 and a value is significantly low if P(x or less) ≤ 0.01. Find the back-to-knee lengths for males, separating significant values from those that are not
Based on Data Set 4 "Births" in Appendix B, birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g. a. For the bell-shaped graph, what is the area under the curve? b. What is the value of the median? c. What is the value of the mode? d. What is the value
Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) ≤ 0.025 and a value is significantly low if P(x or less) ≤ 0.025. Find the female back-to-knee length, separating significant values from those that are not
Disney World requires that people employed as a Mickey Mouse character must have a height between 56 in. and 62 in. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as Mickey Mouse characters? b. If the
The U.S. Air Force once used ACES-II ejection seats designed for men weighing between 140 lb and 211 lb. Given that women's weights are normally distributed with a mean of 171.1 lb and a standard deviation of 46.1 lb (based on data from the National Health Survey), what percentage of women have
The University of Maryland Medical Center considers "low birth weights" to be those that are less than 5.5 lb or 2495 g. Birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g (based on Data Set 4 "Births" in Appendix B). a. If a birth weight is randomly
Refer to Data Set 27 "M&M Weights" in Appendix B and use the weights (grams) of all of the listed M&Ms. a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly normal. b. Treating the unrounded values of the mean and standard deviation as parameters,
For three births, assume that the genders are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of the sample proportions equal the proportion of girls in three births?
A hybridization experiment begins with four peas having yellow pods and one pea having a green pod. Two of the peas are randomly selected with replacement from this population. a. After identifying the 25 different possible samples, find the proportion of peas with yellow pods in each of them, then
The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample. a. Do you think the births are randomly selected with replacement or without replacement? b. Give two reasons why statistical methods tend to be
a. Find the value of the population variance σ2. b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s2. Then combine values of s2 that are the same, as in Table 6-3. c. Find the mean of the
Exercise 9 uses μ = 189 lb, which is based on Data Set 1 "Body Data" in Appendix B. Repeat Exercise 9 using μ = 174 lb (instead of 189 lb), which is the assumed mean weight that was commonly used just a few years ago. What do you conclude about the effect of using an outdated mean that is
Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed. a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement. b. If 4
Quarters are now manufactured so that they have a mean weight of 5.670 g and a standard deviation of 0.062 g, and their weights are normally distributed. A vending machine is configured to accept only those quarters that weigh between 5.550 g and 5.790 g. a. If 1 randomly selected quarter is
Southwest Airlines currently has a seat width of 17 in. Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in. (based on anthropometric survey data from Gordon, Churchill, et al.). a. Find the probability that if an individual man is randomly
In general, what do the symbols μx̅ and σx̅ represent? What are the values of μx̅ and σx̅ for samples of size 64 randomly selected from the population of IQ scores with population mean of 100 and standard deviation of 15?
Annual incomes are known to have a distribution that is skewed to the right instead of being normally distributed. Assume that we collect a large (n > 30) random sample of annual incomes. Can the distribution of incomes in that sample be approximated by a normal distribution because the sample is
The ages of actresses at the times that they won Oscars, as listed in Data Set 14 "Oscar Winner Age" in Appendix B. Refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the
The weights (pounds) of discarded yard waste, as listed in Data Set 31 "Garbage Weight" in Appendix B. Refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the sense that the population
The weights (lb) of the contents in cans of Diet Coke, as listed in Data Set 26 "Cola Weights and Volumes" in Appendix B. Use the data from the indicated exercise in this section. Use software (such as Statdisk, Minitab, Excel, or StatCrunch) or a TI-83, 84 Plus calculator to generate a normal
Exercise 9 "Cookies". In Exercise 9 The numbers of chocolate chips in Chips Ahoy (reduced fat) cookies, as listed in Data Set 28 "Chocolate Chip Cookies" in Appendix B. Use the data from the indicated exercise in this section. Use software (such as Statdisk, Minitab, Excel, or StatCrunch) or a
A sample of arm circumferences (cm) of females from Data Set 1 "Body Data" in Appendix B: 40.7, 44.3, 34.2, 32.5, 38.5. Use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal quantile plot.
A sample of depths (km) of earthquakes is obtained from Data Set 21 "Earthquakes" in Appendix B: 17.3, 7.0, 7.0, 7.0, 8.1, 6.8. Use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then identify the coordinates of each point in the normal
A sample of drive-through service times (seconds) at McDonald's during dinner hours, as listed in Data Set 25 "Fast Food" in Appendix B: 84, 121, 119, 146, 266, 181, 123, 152, 162. Use the given data values to identify the corresponding z scores that are used for a normal quantile plot, then
The numbers of chocolate chips in Chips Ahoy (reduced fat) cookies, as listed in Data Set 28 "Chocolate Chip Cookies" in Appendix B. Refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution. Assume that this requirement is loose in the
In testing the assumption that the probability of a baby boy is 0.512, a geneticist obtains a random sample of 1000 births and finds that 502 of them are boys. Using the continuity correction, describe the area under the graph of a normal distribution corresponding to the following. (For example,
Find the probability that at least 25 cars are black. Is 25 a significantly high number of black cars?Assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors (based on PPG Industries).
Find the probability of exactly 14 red cars. Why can't the result be used to determine whether 14 is a significantly high number of red cars?Assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors
Find the probability of exactly 10 gray cars. Why can't the result be used to determine whether 10 is a significantly low number of gray cars?Assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors
Repeat the preceding exercise after changing the assumed rate of overturned calls from 25% to 22%. Preceding exercise In the year that this exercise was written, there were 879 challenges made to referee calls in professional tennis singles play. Among those challenges, 231 challenges were upheld
Based on an LG smartphone survey, assume that 51% of adults with smartphones use them in theaters. In a separate survey of 250 adults with smartphones, it is found that 109 use them in theaters. a. If the 51% rate is correct, find the probability of getting 109 or fewer smartphone owners who use
Based on a study by Dr. P. Sorita at Indiana University, assume that 12% of us have green eyes. In a study of 650 people, it is found that 86 of them have green eyes. a. Find the probability of at least 86 people with green eyes among 650 randomly selected people. b. Is 86 people with green eyes
Assume that 29.2% of people have sleepwalked (based on "Prevalence and Comorbidity of Nocturnal Wandering in the U.S. Adult General Population," by Ohayon et al., Neurology, Vol. 78, No. 20). Assume that in a random sample of 1480 adults, 455 have sleepwalked. a. Assuming that the rate of 29.2% is
Common tests such as the SAT, ACT, Law School Admission test (LSAT), and Medical College Admission Test (MCAT) use multiple choice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. We want to find the probability of getting at least 25
The probability of a baby being born a boy is 0.512. Consider the problem of finding the probability of exactly 7 boys in 11 births. Solve that problem using (1) normal approximation to the binomial using Table A-2; (2) normal approximation to the binomial using technology instead of Table A-2;
Common tests such as the SAT, ACT, LSAT, and MCAT tests use multiple choice test questions, each with possible answers of a, b, c, d, e, and each question has only one correct answer. For people who make random guesses for answers to a block of 100 questions, identify the values of p, q, μ, and
With n = 20 births and p = 0.512 for a boy, find P(fewer than 8 boys). If the requirements of np ≥ 5 and nq ≥ 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the
With n = 50 guesses and p = 0.2 for a correct answer, find P(exactly 12 correct answers). If the requirements of np ≥ 5 and nq ≥ 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then
Find the probability that fewer than 20 cars are white. Is 20 a significantly low number of white cars?Assume that 100 cars are randomly selected. Refer to the accompanying graph, which shows the top car colors and the percentages of cars with those colors (based on PPG Industries).
The social organization Tall Clubs International has a requirement that women must be at least 70 in. tall. Assume that women have normally distributed heights with a mean of 63.7 in. and a standard deviation of 2.9 in. (based on Data Set 1 "Body Data" in Appendix B). a. Find the percentage of
In designing a security system based on eye (iris) recognition, we must consider the standing eye heights of women, which are normally distributed with a mean of 59.7 in. and a standard deviation of 2.5 in. (based on anthropometric survey data from Gordon, Churchill, et al.). a. If an eye
Consider the same Mark VI monorail described in the preceding exercise. Again assume that heights of men are normally distributed with a mean of 68.6 in. and a standard deviation of 2.8 in. a. In determining the suitability of the monorail door height, why does it make sense to consider men while
Listed below are the recent salaries (in millions of dollars) of players on the San Antonio Spurs professional basketball team. a. Do these salaries appear to come from a population that has a normal distribution? Why or why not? b. Can the mean of this sample be treated as a value from a
a. Find the mean x. b. Find the median. c. Find the standard deviation s. d. Find the variance. e. Convert the highest salary to a z score. f. What level of measurement (nominal, ordinal, interval, ratio) describes this data set? g. Are the salaries discrete data or continuous data? Use the
a. Find Q1, Q2, and Q3.b. Construct a boxplot.c. Based on the accompanying normal quantile plot of the salaries, what do you conclude about the sample of salaries?Use the following recent annual salaries (in millions of dollars) for players on the N.Y. Knicks professional basketball team. 23.4 22.5
Round each of the salaries to the nearest million dollars, then construct a dotplot. Do the values appear to be from a population having a normal distribution? Use the following recent annual salaries (in millions of dollars) for players on the N.Y. Knicks professional basketball team. 23.4 22.5
Assume that 35% of us have blue eyes (based on a study by Dr. P. Soria at Indiana University). a. Let B denote the event of selecting someone who has blue eyes. What does the event B̅ denote? b. Find the value of P(B̅). c. Find the probability of randomly selecting three different people and
Assume that foot lengths of women are normally distributed with a mean of 9.6 in. and a standard deviation of 0.5 in., based on data from the U.S. Army Anthropometry Survey (ANSUR). a. Find the probability that a randomly selected woman has a foot length less than 10.0 in. b. Find the probability
In a study of the accuracy of fast food drive-through orders, McDonald's had 33 orders that were not accurate among 362 orders observed (based on data from QSR magazine). Construct a 95% confidence interval for the proportion of orders that are not accurate.In each case,(a) Find the best point
The drug Eliquis (apixaban) is used to help prevent blood clots in certain patients. In clinical trials, among 5924 patients treated with Eliquis, 153 developed the adverse reaction of nausea (based on data from Bristol-Myers Squibb Co.). Construct a 99% confidence interval for the proportion of
In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 5000 subjects randomly selected from an online group involved with ears. 717 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys.In each case,(a) Find the
A random sample of 860 births in New York State included 426 boys. Construct a 95% confidence interval estimate of the proportion of boys in all births. It is believed that among all births, the proportion of boys is 0.512. Do these sample results provide strong evidence against that belief?
One of Mendel's famous genetics experiments yielded 580 peas, with 428 of them green and 152 yellow. a. Find a 99% confidence interval estimate of the percentage of green peas. b. Based on his theory of genetics, Mendel expected that 75% of the offspring peas would be green. Given that the
In a study of the accuracy of fast food drive-through orders, Burger King had 264 accurate orders and 54 that were not accurate (based on data from QSR magazine). a. Construct a 99% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the result from part (a)
For the poll described in Exercise 1, describe what is meant by the statement that "the margin of error was given as {4 percentage points." Exercise 1 USA Today provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among the 1000 respondents, 14% chose chocolate
The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.). a. Construct a 95% confidence interval estimate
In clinical trials of the drug Lipitor (atorvastatin), 270 subjects were given a placebo and 7 of them had allergic reactions. Among 863 subjects treated with 10 mg of the drug, 8 experienced allergic reactions. Construct the two 95% confidence interval estimates of the percentages of allergic
Before its clinical trials were discontinued, the Genetics & IVF Institute conducted a clinical trial of the XSORT method designed to increase the probability of conceiving a girl and, among the 945 babies born to parents using the XSORT method, there were 879 girls. The YSORT method was designed
In a program designed to help patients stop smoking, 198 patients were given sustained care, and 82.8% of them were no longer smoking after one month. Among 199 patients given standard care, 62.8% were no longer smoking after one month (based on data from "Sustained Care Intervention and
The same study cited in the preceding exercise produced these results after six months for the 198 patients given sustained care: 25.8% were no longer smoking, and these results were biochemically confirmed, but 40.9% of these patients reported that they were no longer smoking. Construct the two
Data Set 27 "M&M Weights" in Appendix B includes data from 100 M&M plain candies, and 19 of them are green. The Mars candy company claims that 16% of its M&M plain candies are green. Use the sample data to construct a 95% confidence interval estimate of the percentage of green M&Ms. What do you
You plan to conduct a survey to estimate the percentage of adults who have had chickenpox. Find the number of people who must be surveyed if you want to be 90% confident that the sample percentage is within two percentage points of the true percentage for the population of all adults. a. Assume
In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.05 margin of error, and use a confidence
A sociologist plans to conduct a survey to estimate the percentage of adults who believe in astrology. How many people must be surveyed if we want a confidence level of 99% and a margin of error of four percentage points? a. Assume that nothing is known about the percentage to be estimated. b. Use
You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95%
You plan to develop a new iOS social gaming app that you believe will surpass the success of Angry Birds and Facebook combined. In forecasting revenue, you need to estimate the percentage of all smartphone and tablet devices that use the iOS operating system versus Android and other operating
An investor is considering funding of a new video game. She wants to know the worldwide percentage of people who play video games, so a survey is being planned. How many people must be surveyed in order to be 90% confident that the estimated percentage is within three percentage points of the true
An epidemiologist plans to conduct a survey to estimate the percentage of women who give birth. How many women must be surveyed in order to be 99% confident that the estimated percentage is in error by no more than two percentage points? a. Assume that nothing is known about the percentage to be
Given specific sample data, such as the data given in Exercise 1, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider? Exercise 1 USA Today provided results from a poll of 1000 adults who were asked to identify their favorite pie. Among
Refer to the accompanying screen display.a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.b. Identify the best point estimate of m and the margin of error.c.
Use these summary statistics for birth weights of 195 boys: x̅ = 32.7 hg, s = 6.6 hg (based on Data Set 4 "Births" in Appendix B). Use a 95% confidence level. Are the results very different from those found in Exercise 9? Does it appear that boys and girls have very different birth
Construct the confidence interval estimate of the mean. Samples of DNA are collected, and the four DNA bases of A, G, C, and T are coded as 1, 2, 3, and 4, respectively. The results are listed below. Construct a 95% confidence interval estimate of the mean. What is the practical use of the
Listed below are amounts of arsenic (μg, or micrograms, per serving) in samples of brown rice from California (based on data from the Food and Drug Administration). Use a 90% confidence level. The Food and Drug Administration also measured amounts of arsenic in samples of brown rice from Arkansas.
In a study of speed dating conducted at Columbia University, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use a 99% confidence level. What do the results tell us about the mean
In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Use a 99% confidence level. Can the result be used to estimate the
An FDA guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D'Agostino, Eli's
a. What is the number of degrees of freedom that should be used for finding the critical value tα/2?b. Find the critical value tα/2 corresponding to a 95% confidence level.c. Give a brief general description of the number of degrees of freedom.Refer to the accompanying screen display that results
Listed below are the amounts of net worth (in millions of dollars) of these ten wealthiest celebrities: Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Construct a 98% confidence interval. What does the
Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7UP, A&W Root Beer, Cherry Coke, . . . , TaB). Use a confidence level of 99%. Does the confidence interval give us good information about the population of all cans of the same 20
Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at the University of Texas at Austin. (See Data Set 17 "Course Evaluations" in Appendix B.) Use a 90% confidence level. What does the confidence interval tell us about the
Listed below are arrival delays (minutes) of randomly selected American Airlines flights from New York (JFK) to Los Angeles (LAX). Negative numbers correspond to flights that arrived before the scheduled arrival time. Use a 95% confidence interval. How good is the on-time performance? -5 -32 -13 -9
Rates Refer to Data Set 1 "Body Data" and construct a 95% confidence interval estimate of the mean pulse rate of adult females; then do the same for adult males. Compare the results.
Refer to Data Set 32 "Airport Data Speeds" and construct a 95% confidence interval estimate of the mean speed for Sprint, then do the same for T-Mobile. Compare the results.
Refer to Data Set 25 "Fast Food" and construct a 95% confidence interval estimate of the mean drive-through service time for McDonald's at dinner; then do the same for Burger King at dinner. Compare the results.
Refer to Data Set 28 "Chocolate Chip Cookies" and construct a 95% confidence interval estimate of the mean number of chocolate chips in Chips Ahoy regular cookies; then do the same for Keebler cookies. Compare the results.
Data Set 1 "Body Data" in Appendix B includes pulse rates of 147 randomly selected adult females, and those pulse rates vary from a low of 36 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult females. Assume that we want 99% confidence that the
Data Set 1 "Body Data" in Appendix B includes pulse rates of 153 randomly selected adult males, and those pulse rates vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the
Data Set 3 "Body Temperatures" in Appendix B includes 106 body temperatures of adults for Day 2 at 12 ²³, and they vary from a low of 96.5∘Fto a high of 99.6∘F. Find the minimum sample size required to estimate the mean body temperature of all adults. Assume that we want 98% confidence that
Construct the confidence interval for Exercise 9 "Birth Weights of Girls," assuming that σ is known to be 7.1 hg.
Construct the confidence interval for Exercise 10 "Birth Weights of Boys," assuming that σ is known to be 6.6 hg.
Use these summary statistics given in Exercise 8: n = 205, x̅ = 30.4 hg, s = 7.1 hg. Use a 95% confidence level. Are the results very different from those found in Example 2 with only 15 sample values? Construct the confidence interval estimate of the mean.
Using all of the brain volumes listed in Data Set 8 "IQ and Brain Size", we get this 95% confidence interval estimate: 9027.8 < σ2 < 33,299.8, and the units of measurement are (cm3)2. Identify the corresponding confidence interval estimate of s and include the appropriate units. Given that the
In a study of speed dating conducted at Columbia University, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a 95% confidence interval estimate of the standard deviation
In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Construct a 95% confidence interval estimate of the standard deviation
Refer to Data Set 17 "Course Evaluations" in Appendix B. a. Use the 93 course evaluations to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained. b. Repeat part (a) using the 93 professor evaluations. c. Compare the results
Refer to Data Set 4 "Births" in Appendix B. a. Use the 205 birth weights of girls to construct a 95% confidence interval estimate of the standard deviation of the population from which the sample was obtained. b. Repeat part (a) using the 195 birth weights of boys. c. Compare the results from part
You want to estimate the standard deviation of the annual incomes of all current statistics students. Find the minimum sample size needed to be 95% confident that the sample standard deviation is within 20% of the population standard deviation. Are those incomes likely to satisfy the requirement of

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