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elementary statistics

Elementary Statistics Using Excel Pearson New 5th Edition Mario F Triola - Solutions

Monorail and Airliner Doors 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 the Appendix: Data Sets).a. What percentage of adult men can fit
Unbiased Estimatorsa. 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
Sampling Distributions 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
Window Placement 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
Door Peephole 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
Bone Density Test 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
What percentage of women have red blood cell counts in the normal range from 4.2 to 5.4?
If 25 women are randomly selected, find the probability that the mean of their red blood cell counts is less than 4.444.
Find the probability that a randomly selected woman has a red blood cell count above the normal range of 4.2 to 5.4.
Find the probability that a randomly selected woman has a red blood cell count below the normal range of 4.2 to 5.4.
For a randomly selected subject, find the probability of a score between 1.37 and 2.42.
For a randomly selected subject, find the probability of a score greater than -1.
Find the score separating the lowest 98% of scores from the highest 2%.
Sketch a graph showing the shape of the distribution of bone density test scores.
Identify the values of m and s for the standard normal distribution.
Overbooking a Boeing 767-300 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
Decision Theory 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
Internet Access 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?
Online TV 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?
Smoking Repeat the preceding exercise after changing the results so that among 50 statistics students, it is found that 3 smoke.
Smoking 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
Cell Phones and Brain Cancer 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
Voters Lying? 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
Washing Hands 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
XSORT Gender Selection 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
Dream Job In a Marist 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
Find the probability that among the 580 offspring peas, 428 or fewer have green pods. Is the result of 428 peas with green pods unusually low?c. Which result is useful for determining whether Mendel’s claimed rate of 75% is incorrect:part (a) or part (b)? Explain.d. Is there strong evidence to
Mendelian 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
Tennis Replay Repeat the preceding exercise after changing the assumed rate of overturned calls from 30% to 33%.
Tennis Replay 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
Probability of exactly 19 voters Voters. In Exercises 9–12, 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
Probability of exactly 23 voters Voters. In Exercises 9–12, 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
Probability that at least 25 voted Voters. In Exercises 9–12, 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
Probability that fewer than 20 voted Voters. In Exercises 9–12, 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
With n = 25 and p = 0.4, find P(more than 9).Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of np Ú 5 and nq Ú 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np 6
With n = 20 and p = 0.8, find P(more than 11).Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of np Ú 5 and nq Ú 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np
With n = 12 and p = 0.7, find P(fewer than 8).Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of np Ú 5 and nq Ú 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np
With n = 13 and p = 0.4, find P(fewer than 3).Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of np Ú 5 and nq Ú 5 are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; if np
Checking Requirement The SAT test uses multiple-choice test questions, each with possible answers ofa, 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
Notation The SAT test uses multiple-choice test questions, each with possible answers ofa,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?
Continuity Correction 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
Exact Value and Approximation Refer to Figure 21 in Example 2, and refer to the display under “Rationale for Using Normal Approximation” It shows the shaded region representing exactly 235 wins among 431 games. What is the shape of the corresponding region in the display? If we use technology
Lognormal Distribution 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?82490 27650 26652
Earthquake Magnitudes Richter scale earthquake magnitudes are listed in Data Set 16 of the Appendix: Data Sets.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
Transformations The heights (in inches) of men listed in Data Set 1 in the Appendix:Data Sets 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
M&M Weights A sample of weights (g) of M&Ms is obtained from those listed in Data Set 20 from the Appendix: Data Sets: 0.864, 0.825, 0.855, 0.942, 0.825, 0.869, 0.912, 0.887, 0.886.
Brain Volumes A sample of human brain volumes (cm3) is obtained from those listed in Data Set 6 from the Appendix: Data Sets: 1272, 1051, 1079, 1034, 1070, 1173, 1079, 1067.
Taxi Out Times 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 the Appendix: Data Sets).
Braking Distances A sample of braking distances (in feet) measured under standard conditions for a sample of large cars from Data Set 14 in the Appendix: Data Sets: 139, 134, 145, 143, 131.
Exercise 12 Using Excel to Generate Normal Q-Q Plots. In Exercises 13–16, use the data from the indicated exercise in this section. Use XLSTAT to generate a normal Q-Q plot. Then determine whether the data come from a normally distributed population.
Exercise 11 Using Excel to Generate Normal Q-Q Plots. In Exercises 13–16, use the data from the indicated exercise in this section. Use XLSTAT to generate a normal Q-Q plot. Then determine whether the data come from a normally distributed population.
Exercise 10 Using Excel to Generate Normal Q-Q Plots. In Exercises 13–16, use the data from the indicated exercise in this section. Use XLSTAT to generate a normal Q-Q plot. Then determine whether the data come from a normally distributed population.
Exercise 9 Using Excel to Generate Normal Q-Q Plots. In Exercises 13–16, use the data from the indicated exercise in this section. Use XLSTAT to generate a normal Q-Q plot. Then determine whether the data come from a normally distributed population.
Secondhand Smoke The cotinine measurements of nonsmokers who were exposed to tobacco smoke at home or work, as listed in Data Set 9 in the Appendix: Data Sets. Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population
Blood Pressure The systolic blood pressure measurements of males as listed in Data Set 1 in the Appendix: Data Sets. Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution.Assume that this
Heights of Presidents The heights (cm) of the presidents of the United States as listed in Data Set 12 in the Appendix: Data Sets. Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal
Flight Arrival Delays The arrival delay times (minutes) as listed in Data Set 15 in the Appendix: Data Sets. Determining Normality. In Exercises 9–12, refer to the indicated sample data and determine whether they appear to be from a population with a normal distribution.Assume that this
Small Sample An article includes elapsed times (hours) to lumbar puncture for 19 patients who entered emergency rooms with sudden and severe “thunderclap” headaches (based on data from “Thunderclap Headache and Normal Computed Tomographic Results: Value of Cerebrospinal Fluid Analysis,” by
Normal Quantile Plot After constructing a histogram of the ages of the 40 women included in Data Set 1 in the Appendix: Data Sets, you see that the histogram is far from being bell-shaped. What do you now know about the normal quantile plot?
Normal Quantile Plot Data Set 1 in the Appendix: Data Sets includes the heights of 40 randomly selected women. If you were to construct a histogram of those heights, what shape do you expect the histogram to have? If you were to construct a normal quantile plot of those heights, what pattern would
Correcting for a Finite Population 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
Correcting for a Finite Population 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 m = 95.5 and s = 16.0 (based on data from “Neurobehavioral Outcomes of School-age Children Born Extremely
Loading Aircraft 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
Doorway Height 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 the Appendix: Data Sets).a. If a male passenger is randomly
Loading a Tour Boat 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
Redesign of Ejection Seats 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
Pulse Rates of Women 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 (based on Data Set 1 in the Appendix: Data Sets).a. Find the percentiles P1 and P99.b. Dr. Puretz sees exactly 25 female patients each
Gondola Safety 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
Loading M&M Packages 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 the Appendix: Data Sets). 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.
Water Taxi Safety 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
Designing Manholes 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
Designing Hats 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 produces women’s hats so that they fit head
Elevator Safety Exercise 11 uses m = 182.9 lb, which is based on Data Set 1 in the Appendix: Data Sets. Repeat Exercise 11 using m = 174 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,
Elevator Safety 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
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.
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.
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), even
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), even
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.
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.
Lottery Numbers 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?
Notation 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 mx and sx represent, and what are
Small Sample Heights of adult females are normally distributed. Samples of heights of adult females, each of size n = 3, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as a normal distribution because the sample size is too
Standard Error of the Mean The population of current statistics students has ages with mean m and standard deviation s. 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
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? (Hint: See Example 5.)
Quality Control 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
SAT and ACT Tests 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
Births: Sampling Distribution of Sample Proportion 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
Births: Sampling Distribution of Sample Proportion 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
Sampling Distribution of the Variance Repeat Exercise 11 using variances instead of means.
Sampling Distribution of the Range Repeat Exercise 11 using ranges instead of means.
Sampling Distribution of the Median Repeat Exercise 11using medians instead of means.
Sampling Distribution of the Sample Meana. 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. (Hint: See Table 4 in
Sampling Distribution of the Sample Proportiona. For the population, find the proportion of odd numbers.b. Table 3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample proportion of odd numbers.Then combine values of
Sampling Distribution of the Sample Mediana. Find the value of the population median.b. Table 3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample median. Then combine values of the median that are the same, as in
(Hint: See Example 1 for Tables 3 and 4 that describe the sampling distribution of the sample mean.)c. Find the mean of the sampling distribution of the sample standard deviation.d. Based on the preceding results, is the sample standard deviation an unbiased estimator of the population standard
Sampling Distribution of the Sample Standard Deviation For the following, round results to three decimal places.a. Find the value of the population standard deviation s.b. Table 3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling
Sampling Distribution of the Sample Variancea. Find the value of the population variance s2.b. Table 3 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
Lottery Results Many states have a Pick 3 lottery in which three digits are randomly selected each day. Winning requires that you select the same three digits in the same order that they are drawn. Assume that you compute the mean of each set of three selected digits.a. What is the approximate
Good Sample? For the population of all college students currently taking a statistics course, you want to estimate the proportion who are women. You obtain a simple random sample of statistics students at Broward College in Florida. Is the resulting sample proportion a good estimator of the

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