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Elementary Statistics 12th Edition Mario F. Triola - Solutions

a. After identifying the 16 different possible samples, find the mean of each sample, then construct a table representing the sampling distribution of the sample mean. In the table, combine values of the sample mean that are the same.b. Compare the mean of the population {56, 49, 58, 46} to the
Repeat Exercise using medians instead of means.Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.In exercise, a. After
Repeat Exercise using ranges instead of means.Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.In exercise,a. After identifying
Repeat Exercise using variances instead of means.Use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.In exercise, a. After
When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal
When three births are randomly selected, the sample space for genders is bbb, bbg, bgb, bgg, gbb, gbg, ggb, and ggg. Assume that those eight outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from three births. Does the mean of
Because they enable efficient procedures for evaluating answers, multiple-choice questions are commonly used on standardized tests, such as the SAT or ACT. Such questions typically have five choices, one of which is correct. Assume that you must make random guesses for two such questions. Assume
After constructing a new manufacturing machine, five prototype integrated circuit chips are produced and it is found that two are defective (D) and three are acceptable (A). Assume that two of the chips are randomly selected with replacement from this population.a. After identifying the 25
Exercise requires the construction of a table that describes the sampling distribution of the proportions of girls from two births. Consider the formula shown here, and evaluate that formula using sample proportions x of 0, 0.5, and 1. Based on the results, does the formula describe the sampling
Mean Absolute Deviation Is the mean absolute deviation of a sample a good statistic for estimating the mean absolute deviation of the population? Why or why not?
The population of current statistics students has ages with mean m and standard deviations. Samples of statistics students are randomly selected so that there are exactly 40 students in each sample. For each sample, the mean age is computed. What does the central limit theorem tell us about the
The population of distances that adult females can reach forward is normally distributed with a mean of 60.5 cm and a standard deviation of 6.6 cm (from the Federal Aviation Administration). If samples of 36 adult females are randomly selected, what do μx and σx represent, and what are their
In each drawing for the Texas Pick 3 lottery, three digits between 0 and 9 inclusive are randomly selected. What is the distribution of the selected digits? If the mean is calculated for each drawing, can the distribution of the sample means be treated as a normal distribution?
a. If 1 adult female is randomly selected, find the probability that her overhead reach is less than 222.7 cm. b. If 49 adult females are randomly selected, find the probability that they have a mean overhead reach less than 207.0 cm. Use this information about the overhead reach distances of adult
a. If 1 adult female is randomly selected, find the probability that her overhead reach is less than 196.9 cm. b. If 36 adult females are randomly selected, find the probability that they have a mean overhead reach less than 205.0 cm. Use this information about the overhead reach distances of adult
a. If 1 adult female is randomly selected, find the probability that her overhead reach is greater than 218.4 cm. b. If 9 adult females are randomly selected, find the probability that they have a mean overhead reach greater than 204.0 cm. c. Why can the normal distribution be used in part (b),
a. If 1 adult female is randomly selected, find the probability that her overhead reach is greater than 195.0 cm. b. If 25 adult females are randomly selected, find the probability that they have a mean overhead reach greater than 203.0 cm. c. Why can the normal distribution be used in part (b),
a. If 1 adult female is randomly selected, find the probability that her overhead reach is between 179.7 cm and 231.3 cm. b. If 40 adult females are randomly selected, find the probability that they have a mean overhead reach between 204.0 cm and 206.0 cm. Use this information about the overhead
a. If 1 adult female is randomly selected, find the probability that her overhead reach is between 180.0 cm and 200.0 cm. b. If 50 adult females are randomly selected, find the probability that they have a mean overhead reach between 198.0 cm and 206.0 cm. Use this information about the overhead
Example 2 referred to an Ohio elevator with a maximum capacity of 2500 lb. When rating elevators, it is common to use a 25% safety factor, so the elevator should actually be able to carry a load that is 25% greater than the stated limit. The maximum capacity of 2500 lb becomes 3125 lb after it is
Exercise 11 uses m182.9 lb, which is based on Data Set 1 in Appendix B. Repeat Exercise 11 using m174 lb (instead of 182.9 lb), which is the assumed mean weight that was commonly used just a few years ago. Assuming that the mean weight of males is now 182.9 lb, not the value of 174 lb that was used
Women have head circumferences that are normally distributed with a mean of 22.65 in. and a standard deviation of 0.80 in. (based on data from the National Health and Nutrition Examination Survey).a. If the Hats by Leko Company produce women’s hats so that they fit head circumferences between
According to the web site www.torchmate.com, “manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter.” Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder breadths that are normally distributed
Passengers died when a water taxi sank in Baltimore’s Inner Harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a
M&M plain candies have a mean weight of 0.8565 g and a standard deviation of 0.0518 g (based on Data Set 20 in Appendix B). The M&M candies used in Data Set 20 came from a package containing 465 candies, and the package label stated that the net weight is 396.9 g. (If every package has 465 candies,
A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater than 2004>12 = 167 lb. Because men tend to weigh more than women, a
Women have pulse rates that are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute. a. Find the percentiles P1 and P99. b. Dr. Puretz sees exactly 25 female patients each day. Find the probability that 25 randomly selected women have a mean
When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. Weights of women are now normally distributed with a
The Ethan Allen tour boat capsized and sank in Lake George, New York, and 20 of the 47 passengers drowned. Based on a 1960 assumption of a mean weight of 140 lb for passengers, the boat was rated to carry 50 passengers. After the boat sank, New York State changed the assumed mean weight from 140 lb
The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.5 in. and a standard deviation of 2.4 in. (based on Data Set 1 in Appendix B). a. If a male passenger is randomly selected, find the probability that
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The Bombardier Dash 8 aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6200 lb. The pilot sees that the
In a study of babies born with very low birth weights, 275 children were given IQ tests at age 8, and their scores approximated a normal distribution with µ = 95.5 and σ = 16.0 (based on data from “Neurobehavioral Outcomes of School-age Children Born Extremely Low Birth Weight or Very
The Orange County Spa began with 300 members. Those members had weights with a distribution that is approximately normal with a mean of 177 lb and a standard deviation of 40 lb. The facility includes an elevator that can hold up to 16 passengers. a. When considering the distribution of sample means
Use the same population of {4, 5, 9} from Example 1 in Section 6-4. Assume that samples of size n = 2 are randomly selected without replacement.a. Find µ and Ïƒ for the population.b. After finding all samples of size n = 2 that can be obtained without replacement, find the population of all
The arrival delay times (minutes) as listed in Data Set 15 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 distribution need not be
The heights (cm) of the presidents of the United States as listed in Data Set 12 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 systolic blood pressure measurements of males as listed in Data Set 1 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 distribution need
The continue measurements of nonsmokers who were exposed to tobacco smoke at home or work, as listed in Data Set 9 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
Exercise in exercise Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a TI-83/84 Plus calculator to generate a normal quantile plot. Then determine whether the data come from a normally distributed population.
Exercise In exercise, Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a TI-83/84 Plus calculator to generate a normal quantile plot. Then determine whether the data come from a normally distributed population. Use
Exercise Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel or StatCrunch) or a TI-83/84 Plus calculator to generate a normal quantile plot. Then determine whether the data come from a normally distributed population.
Exercise In exercise, Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a TI-83/84 Plus calculator to generate a normal quantile plot. Then determine whether the data come from a normally distributed population.
A sample of braking distances (in feet) measured under standard conditions for a sample of large cars from Data Set 14 in Appendix B: 139, 134, 145, 143, 131. Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel or StatCrunch) or a
A sample of flights is selected, and the times (minutes) required to taxi out for takeoff are 37, 13, 14, 15, 31, 15 (from Data Set 15 in Appendix B). Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a TI-83/84 Plus
A sample of human brain volumes (cm3) is obtained from those listed in Data Set 6 from Appendix B: 1272, 1051, 1079, 1034, 1070, 1173, 1079, 1067. Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a TI-83/84 Plus
A sample of weights (g) of M&Ms is obtained from those listed in Data Set 20 from Appendix B: 0.864, 0.825, 0.855, 0.942, 0.825, 0.869, 0.912, 0.887, 0.886. Use the data from the indicated exercise in this section. Use computer software (such as STATDISK, Minitab, Excel, or StatCrunch) or a
The heights (in inches) of men listed in Data Set 1 in Appendix B have a distribution that is approximately normal, so it appears that those heights are from a normally distributed population. a. If 2 inches is added to each height, are the new heights also normally distributed? b. If each height
Richter scale earthquake magnitudes are listed in Data Set 16 of Appendix B. a. Determine whether those magnitudes are from a population with a normal distribution. b. For the Richter scale, assume that the magnitude of the energy from an earthquake is first measured, then the logarithm (base 10)
The following are the values of net worth (in thousands of dollars) of the members of the executive branch of the current U.S. government. Test these values for normality, then take the logarithm of each value and test for normality. What do you conclude?
Refer to Figure in Example 2, and refer to the Minitab display near the beginning of this section. Figure shows the shaded region representing exactly 235 wins among 431 games. What is the shape of the corresponding region in the Minitab display? If we use technology without an approximation, the
In a preliminary test of the MicroSort method of gender selection, 14 couples were treated and 13 of them had baby girls. If we plan to use the normal approximation to the binomial distribution for finding the probability of exactly 13 girls (assuming that the probability of a girl is 0.5), what is
The SAT test uses 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 25 questions, identify the values of p, q, m, and s. What do m and s measure?
The SAT test uses 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 exactly 10 correct answers for someone who makes random guesses for answers to a block of 25 questions. If we plan
With n = 13 and p = 0.4, find P(fewer than 3). 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 normal approximation should not
With n = 25 and p = 0.4, find P(more than 9). 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 normal approximation should not
Probability that fewer than 20 voted use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of
Probability that at least 25 voted use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of
Probability of exactly 23 voters use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of them
Probability of exactly 19 voters use a normal approximation to find the probability of the indicated number of voters. In each case, assume that 100 eligible voters aged 18–24 are randomly selected. The most recent Census Bureau results show that among eligible voters aged 18–24, 22% of
In the year that this exercise was written, there were 611 challenges made to referee calls in professional tennis singles play. Among those challenges, 172 were upheld with the call overturned. Assume that 30% of the challenges are successfully upheld with the call overturned. a. Find the
Repeat the preceding exercise after changing the assumed rate of overturned calls from 30% to 33%.In preceding exercise, In the year that this exercise was written, there were 611 challenges made to referee calls in professional tennis singles play. Among those challenges, 172 were upheld with the
Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 580 peas, with 428 of them having green pods. If we assume, as Mendel did, that under these circumstances, there is a 3>4 probability that a pea will have a green pod, we would expect that
College poll of 1004 adults, 291 chose professional athlete as their dream job. Assume that 25% of adults consider being a professional athlete their dream job. a. The result of 291 is more than 25% of 1004, so find the probability that among 1004 random adults, 291 or more consider being a
MicroSort’s XSORT gender-selection technique is designed to increase the likelihood that a baby will be a girl. In updated results (as of this writing) of the XSORT gender-selection technique, 945 births consisted of 879 baby girls and 66 baby boys (based on data from the Genetics & IVF
Based on observed males using public restrooms, 85% of adult males wash their hands in a public restroom (based on data from the American Society for Microbiology and the American Cleaning Institute). In a survey of 523 adult males, 518 reported that they wash their hands in a public restroom.
In a survey of 1002 people, 701 said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote. Given that 61% of eligible voters actually did vote, find the probability that among 1002 randomly
In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. Assuming that the use of cell phones has no effect on developing such cancers, there is a 0.000340 probability of a person developing cancer of the brain or nervous system. We
Based on a recent Harris Interactive survey, 20% of adults in the United States smoke. In a survey of 50 statistics students, it is found that 6 of them smoke. Find the probability that should be used for determining whether the 20% rate is correct for statistics students. What do you conclude?
Repeat the preceding exercise after changing the results so that among 50 statistics students, it is found that 3 smoke.
In a Comcast survey of 1000 adults, 17% said that they watch prime-time TV online. If we assume that 20% of adults watch prime-time TV online, find the probability that should be used to determine whether the 20% rate is correct or whether it should be lower than 20%? What do you conclude?
Of U.S. households, 67% have Internet access (based on data from the Census Bureau). In a random sample of 250 households, 70% are found to have Internet access. Find the probability that should be used to determine whether the 67% rate is too low. What do you conclude?
Marc Taylor plans to place 200 bets of $5 each on a game at the Mirage casino in Las Vegas. a. One strategy is to bet on the number 7 at roulette. A win pays off with odds of 35:1 and, on any one spin, there is a probability of 1>38 that 7 will be the winning number. Among the 200 bets, what is the
A Boeing 767-300 aircraft has 213 seats. When someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an IBM research paper by Lawrence, Hong, and Cherrier). How many reservations could be accepted for a Boeing 767-300
A bone mineral density test is used to identify a bone disease. The result of a bone density test is commonly measured as a z score, and the population of z scores is normally distributed with a mean of 0 and a standard deviation of 1. a. For a randomly selected subject, find the probability of a
Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard deviation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al.). a. A door peephole is placed at a height that is uncomfortable for women with standing eye heights greater than 1605
Standing eye heights of men are normally distributed with a mean of 1634 mm and a standard deviation of 66 mm (based on anthropometric survey data from Gordon, Churchill, et al.). a. If a window is positioned so that it is comfortable for men with standing eye heights greater than 1500 mm, what
Scores on the ACT test have a distribution that is approximately normal with mean 21.1 and standard deviation 5.1. A sample of 80 ACT scores is randomly selected and the sample mean is computed. a. Describe the distribution of such sample means. b. What is the mean of all such sample means? c. What
a. What is an unbiased estimator? b. For the following statistics, identify those that are unbiased estimators: mean median, range, variance, proportion. c. Determine whether the following statement is true or false: “The sample standard deviation is a biased estimator, but the bias is relatively
The Mark VI monorail used at Disney World has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.5 in. and a standard deviation of 2.4 in. (based on Data Set 1 in Appendix B). a. What percentage of adult men can fit through the doors without bending? Does the
Under older Federal Aviation Administration rules, airlines were required to estimate the weight of a passenger as 185 lb. (That amount is for an adult traveling in winter, and it includes 20 lb of carry-on baggage.) Rules were revised to use an estimate of 195 lb. Men now have weights that are
Listed below are the current salaries (in thousands of dollars) of players on the New York Yankees baseball 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 population having a
In one of Mendel’s experiments with plants, 1064 offspring consisted of 787 plants with long stems. According to Mendel’s theory, 3>4 of the offspring plants should have long stems. Assuming that Mendel’s proportion of 3>4 is correct, find the probability of getting 787or fewer plants with
There is an 80% chance that a prospective employer will check the educational background of a job applicant (based on data from the Bureau of National Affairs, Inc.). Sixty-four job applications are randomly selected. a. Find the probability that at least 50 of the applicants have their educational
The following are current annual salaries (in thousands of dollars) for the starting players on the Miami Heat basketball team: 14,500, 14,500, 14,000, 5000, 3500.a. Find the mean x and express the result in dollars instead of thousands of dollars.b. Find the median and express the result in
Assume that 10% of us believe that college is not a good investment (based on a survey in USA Today). a. Let A denote the event of selecting someone who believes that college is not a good investment. What does the event A denote? b. Find the value of P(A). c. Find the probability of randomly
Birth weights in the United States have a distribution that is approximately normal with a mean of 3369 g and a standard deviation of 567 g (based on data from “Comparison of Birth Weight Distributions between Chinese and Caucasian Infants,” by Wen, Kramer, Usher, American Journal of
The accompanying graph is a histogram of ages of U.S. presidents at the time they were inaugurated (from Data Set 12 in Appendix B).a. Identify two features of the vertical scale that cause the graph to be somewhat misleading.b. Does the histogram appear to show data from a population having a
According to data from the American Medical Association, 10% of us are left-handed. a. If three people are randomly selected, find the probability that they are all left-handed. b. If three people are randomly selected, find the probability that at least one of them is left handed. c. Why can’t
For the poll described in Exercise, describe what is meant by the statement that “the margin of error is {3 percentage points.”
For the poll described in Exercise, what do pn, qn, n, E, and p represent? If the confidence level is 95%, what is the value of a?
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?
Froma KRC Research poll in which respondents were asked if they felt vulnerable to identify theft: n = 1002, x = 531 who said “yes.” Use a 95% confidence level. Use the given sample data and confidence level. In each case, (a) Find the best point estimate of the population proportion p; (b)
From a 3M Privacy Filters poll in which respondents were asked to identify their favorite seat when they fly: n = 806, x = 492 who chose the window seat. Use a 99% confidence level. Use the given sample data and confidence level. In each case, (a) Find the best point estimate of the population
From a Prince Market Research poll in which respondents were asked if they acted to annoy a bad driver: n = 2518, x = 1083 who said that they honked. Use a 90% confidence level. Use the given sample data and confidence level. In each case, (a) Find the best point estimate of the population
From an Angus Reid Public Opinion poll in which respondents were asked if they felt that U.S. nuclear weapons made them feel safer: n = 1005, x = 543 who said “yes.” Use a confidence level of 80%. Use the given sample data and confidence level. In each case, (a) Find the best point estimate of
The Genetics and IVF Institute conducted clinical trial of the XSORT method designed to increase the probability of conceiving a girl. As of this writing, 945 babies were born to parents using the XSORT method, and 879 of them were girls. a. What is the best point estimate of the population
The Genetics and IVF Institute conducted clinical trial of the YSORT method designed to increase the probability of conceiving a boy. As of this writing, 291 babies were born to parents using the YSORT method, and 239 of them were boys. a. What is the best point estimate of the population
When she was 9 years of age, Emily Rosa did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped coin to select either her right hand or her left hand then she asked the therapists to identify the selected hand by
When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. a. Find a 95% confidence interval estimate of the percentage of yellow peas. b. Based on his theory of genetics, Mendel expected that 25% of the offspring peas
Online Books A Consumer Reports Research Center survey of 427 women showed that 29.0% of them purchase books online. a. Among the 427 women who were surveyed, what is the number of women who said that they purchase books online? b. Find a 95% confidence interval estimate of the percentage of all

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