Question: Suppose that A and B are mutually

> Express the kth percentile, Pk, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.

> Express the quartiles, Q1, Q2, and Q3, of a normally distributed variable in terms of its mean, μ, and standard deviation, σ.

> Let 0

> Desert Samaritan Hospital in Mesa, Arizona, keeps records of emergency room traffic. Those records reveal that the times between arriving patients have a mean of 8.7 minutes with a standard deviation of 8.7 minutes. Based solely on the values of these tw

> The rare booted eagle of western Europe was the focus of a study by S. Suarez et al. to identify optimal nesting habitat for this raptor. According to their paper “Nesting Habitat Selection by Booted Eagles (Hieraaetus pennatus) and Implications for Mana

> In a designed experiment, there are two factors, say, Factor A and Factor B. Factor A has four levels, say, a1, a2, a3, and a4; Factor B has two levels, say, b1 and b2. a. Construct a schematic for the treatments. b. Use part (a) to determine the number

> A sample of fifth-grade classes was studied in the journal article “Predicting Feelings of School Safety for Lower, Middle, and Upper School Students” (Applied Psychology in Criminal Justice, Vol. 7, Issue 2, pp. 59–76) by R. Bachman et al. One of the va

> In the article “Are Christian/Religious People Poor Tippers?” (Journal of Applied Social Psychology, Vol. 43, Issue 5, pp. 928–935), M. Lynn and B. Katz report that, for customers who receive bad service, the mean percentage tip is 8.56% of the bill with

> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. Given that 28.4% of all possible observations of the variable are less than 11, determine the area under the density

> Researchers S. Lesik and M. Mitchell explore the difficulty of predicting success in college-level mathematics in the article “The Investigation of Multiple Paths to Success in College-Level Mathematics” (Journal of Applied Research in Higher Education,

> Research reveals that foot length of women is normally distributed with mean 9.58 inches and standard deviation 0.51 inch. This distribution is useful to shoe manufacturers, shoe stores, and related merchants because it permits them to make informed deci

> Refer to Example. The heights of the 3264 female students attending midwestern college are approximately normally distributed with mean 64.4 inches and standard deviation 2.4 inches. Thus, we can use the normal distribution with μ = 64.4 and σ = 2.4 to a

> The A. C. Nielsen Company reported in the Nielsen Report on Television that the mean weekly television viewing time for children aged 2–6 years is 24.85 hours. Assume that the weekly television viewing times of such children are normally distributed with

> In 1905, R. Pearl published the article “Bio metrical Studies on Man. I. Variation and Correlation in Brain Weight” (Biometrika, Vol. 4, pp. 13–104). According to the study, brain weights of Swedish men are normally distributed with mean 1.40 kg and stan

> In the article “Assessing Friendship Motivation During Preadolescence and Early Adolescence” (Journal of Early Adolescence, Vol. 25, No. 3, pp. 367–385), J. Richard and B. Schneider described the properties of the Friendship Motivation Scale for Children

> A preliminary behavioral study of the Jingdong black gibbon, a primate endemic to the Wuliang Mountains in China, found that the mean song bout duration in the wet season is 12.59 minutes with a standard deviation of 5.31 minutes. [SOURCE: L. Sheeran et

> G. Wittemeyer et al. studied demographic data on African elephants living in Kenya in the article “Comparative Demography of an At-Risk African Elephant Population” (PLOS ONE, Vol. 8. No. 1). Based on this study, we will assume that the time between preg

> One of the larger species of tarantulas is the Grammostola mollicoma, whose common name is the Brazilian giant tawny red. A tarantula has two body parts. The anterior part of the body is covered above by a shell, or carapace. F. Costa and F. Perez–Miles

> In a designed experiment, there are two factors, say, Factor A and Factor B. Factor A has three levels, say, a1, a2, and a3; Factor B has four levels, say, b1, b2, b3, and b4. a. Construct a schematic for the treatments similar to Table 1.8 on page 27. b

> Umbilical cord blood analysis immediately after delivery is one way to measure the health of an infant after birth. Researchers G. Natalucci et al. used it as a predictor of brain maturation of preterm infants in the article “Functional Brain Maturation

> From the paper “Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis” (Aquaculture, Vol. 242, No. 1–4, pp. 357– 363) by S. Siikavuopio et al., we found that weights of adult green sea urchins are norma

> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. Given that 33.6% of all possible observations of the variable exceed 8, determine the area under the density curve th

> What is a density curve?

> The National Center for Education Statistics publishes information about school enrollment in Digest of Education Statistics. According to that document, 85.3% of students attend public schools, 27.9% of students attend college, and 20.1% of students att

> According to America’s Families and Living Arrangements, published by the U.S. Census Bureau, 51.5% of U.S. adults are female, 10.4% of U.S. adults are divorced, and 6.0% of U.S. adults are divorced females. For a U.S. adult selected at random, let F = e

> In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible. Let A = event the sum of the dice is 7, B = event the sum of the dice is 11, C = event the sum of the dice is 2, D = event the sum of the dice is 3,

> The U.S. Bureau of Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. Following is an age distribution for persons naturalized during one year. Suppose that one of these naturalized pe

> The Association of American Universities published a report titled “Looking More Closely at Student Debt.” This report explores the issue of the cost of a college education and its impact on student loan debt. Using information from a credit reporting co

> We have provided simple data sets for you to practice the basics of finding measures of center. 4, 2, 0, 2, 2 a. mean. b. median. c. mode(s).

> Use the complementation rule to find the probability that one of these Type 4A development corporations selected at random has receipts a. of at least $25,000. b. less than $500,000.

> In a designed experiment, there is one factor with five levels. How many treatments are there?

> Use the complementation rule to find the probability that a randomly selected U.S. senator is a. 50 years old or older. b. under 70 years old.

> According to the Religious Landscape Survey, sponsored by the Pew Forum on Religion and Public Life, a distribution of religious affiliation among U.S. adults is as shown in the following table. Find the probability that the religious affiliation of a ra

> From the document “Computer and Internet Use in the United States: Population Characteristics” (Current Population Survey) by T. File, we obtained the following percentage distribution of household income for U.S. households with Internet access. Suppose

> The U.S. Coast Guard maintains a database of the number, source, and location of oil spills in U.S. navigable and territorial waters. The following is a probability distribution for location of oil spill events. Apply the special addition rule to find th

> Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability of being dealt a pocket pair in Texas hold’em is 0.059. b. If a balanced dime is tossed three times, the probability that it w

> The National Institute on Drug Abuse issued the report Monitoring the Future, which addressed the issue of drinking, cigarette, and smokeless tobacco use for eighth, tenth, and twelfth graders. During one year, 12,900 twelfth graders were asked the quest

> The State of Texas maintains records pertaining to the economic development of corporations in the state. From the Economic Development Corporation Report, published by the Texas Comptroller of Public Accounts, we obtained the following frequency distrib

> According to the Congressional Directory, the official directory of the U.S. Congress, prepared by the Joint Committee on Printing, the age distribution for senators in the U.S. Congress as of Fall 2013, is as shown in the following table. Suppose that a

> R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper “Ethiopian-Born and Native Israeli School Children Have Different Growth Patterns” (Nutrition, Vol. 19, pp. 427– 431). The study,

> Suppose that A and B are events such that P(A) = 1/4, P(B) = 1/3, and P(A or B) = 1/2. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(A & B).

> Suppose that A and B are events such that P(A) = 1/3, P(A or B) = 1/2, and P(A & B) = 1/10. a. Are events A and B mutually exclusive? Explain your answer. b. Find P(B).

> In a designed experiment, there is one factor with four levels. How many treatments are there?

> Suppose that A and B are events such that P(A) = 0.84, P(B) = 0.46, and P(A & B) = 0.38. Determine P(A or B).

> Suppose that C and D are events such that P(C) = 0.35, P(D) = 0.40, and P(C & D) = 0.30. Determine P(C or D).

> Let F be an event with probability 0.72. Find the probability of (not F).

> Let E be an event with probability 0.35. Find the probability of (not E).

> Suppose that C and D are mutually exclusive events such that P(C) = 0.14 and P(D) = 0.32. Determine P(C or D).

> Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability is 0.487 that a newborn baby will be a girl. b. The probability of a single ticket winning a prize in the Powerball lottery is

> The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 miles per hour (mph) and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Env

> A bowl contains 12 poker chips—3 red, 4 white, and 5 blue. One of these poker chips is selected at random from the bowl. Let B denote the event that the chip selected is blue. Find the probability that a blue chip is selected, and express your answer in

> An ordinary deck of playing cards has 52 cards. There are four suits—spades, hearts, diamonds, and clubs— with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. One of these cards is selected at random. Let R denote the even

> Let A, B, and C be events of a sample space. Complete the following table.

> In this section, we discussed two types of statistical designs. Identify and explain the meaning of each one.

> Suppose that A, B, and C are three events that cannot all occur simultaneously. Does this condition necessarily imply that A, B, and C are mutually exclusive? Justify your answer and illustrate it with a Venn diagram.

> Construct a Venn diagram that portrays four events, A, B, C, and D that have the following properties: Events A, B, and C are mutually exclusive; events A, B, and D are mutually exclusive; no other three of the four events are mutually exclusive.

> Let A and B be events of a sample space. a. Suppose that A and (not B) are mutually exclusive. Explain why B occurs whenever A occurs. b. Suppose that B occurs whenever A occurs. Explain why A and (not B) are mutually exclusive.

> From 10 men and 8 women in a pool of potential jurors, 12 are chosen at random to constitute a jury. Suppose that you observe the number of men who are chosen for the jury. Let A be the event that at least half of the 12 jurors are men, and let B be the

> Consider the following random experiment: First, roll a die and observe the number of dots facing up; then, toss a coin the number of times that the die shows and observe the total number of heads. Thus, if the die shows three dots facing up and the coin

> Refer to Exercise 5.66. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive. Data from Exercise 5.66: A survey was conducted in Canada to ascertain public opinion about a major national park region in the Banf

> A study by researchers at the University of Maryland addressed the question of whether the mean body temperature of humans is 98.6◦F. The results of the study by P. Mackowiak et al. appeared in the article “A Critical Appraisal of 98.6◦F, the Upper Limit

> State the frequentist interpretation of probability.

> Refer to Exercise 5.65. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive. Data from Exercise 5.65: The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. Th

> Each part of this exercise contains events from Exercise 5.54. In each case, decide whether the events are mutually exclusive. a. A and B b. B and C c. A, B, and C d. A, B, and D e. A, B, C, and D

> Refer to Exercise 5.53. a. Are events A and B mutually exclusive? b. Are events B and C mutually exclusive? c. Are events A, C, and D mutually exclusive? d. Are there three mutually exclusive events among A, B, C, and D? four? Data from Exercise 5.53: W

> Define each of the following terms in the context of experimental design. a. Response variable b. Factor c. Levels d. Treatments

> A survey was conducted in Canada to ascertain public opinion about a major national park region in the Banff-Bow Valley. One question asked the amount that respondents would be willing to contribute per year to protect the environment in the Banff-Bow Va

> The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands. For a U.S. hou

> The NBA Finals of basketball is played in a best of seven series. The number of games necessary to decide a winner can range from four to seven. Wikipedia lists the NBA Finals winners and number of games played per series. The following table provides th

> The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919–1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document Wo

> The following table provides a frequency distribution for the ages of adult women seeking pregnancy tests at public health facilities in Missouri during a 3-month period. It appeared in the article “Factors Affecting Contraceptive Use in Women Seeking Pr

> Body mass index (BMI) is a measure of body fat based on height and weight. According to the document Dietary Guidelines for Americans published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI

> In a report titled Behavioral Risk Factor Surveillance System Summary Prevalence Report, the Centers for Disease Control and Prevention discusses the prevalence of diabetes in the United States. The following table provides a diabetes prevalence frequenc

> For each of the following events, list the outcomes that constitute the event, and describe the event in words. a. (not B) b. (A & B) c. (C or D)

> An experiment has 40 possible outcomes, all equally likely. An event can occur in 25 ways. The probability that the event occurs is____.

> For each of the following events, list the outcomes that constitute the event, and describe the event in words. a. (not A) b. (B & D) c. (B or C)

> For each of the following events, list the outcomes that constitute the event and describe the event in words. a. (not C) b. (C & D) c. (A or C)

> State and explain the significance of the three basic principles of experimental design.

> We presented cognition data obtained by researchers studying the effects of early postnatal dexamethasone therapy for the prevention or treatment of chronic lung disease of prematurity. The study included 146 school-age children of which 72 had been in a

> For each of the following events, list the outcomes that constitute the event and describe the event in words. a. (not A) b. (A & B) c. (B or C)

> When a dime is tossed four times, there are the following 16 possible outcomes. Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each

> A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing s

> The inferential procedures discussed in this book are intended for use with only one particular sampling procedure. What sampling procedure is that?

> Construct a dotplot for the following exam scores of the students in an introductory statistics class.

> In a horse race, the odds against winning are as shown in the following table. For example, the odds against winning are 8 to 1 for horse #1. List the outcomes constituting A = event one of the top two favorites wins (the top two favorites are the two ho

> When one die is rolled, the following six outcomes are possible: List the outcomes constituting A = event the die comes up even, B = event the die comes up 4 or more, C = event the die comes up at most 2, and D = event the die comes up 3.

> Draw a Venn diagram portraying four mutually exclusive events.

> Answer true or false to the following statement and justify your answer: If event A and event B are mutually exclusive, so are events A, B, and C for every event C.

> Answer true or false to the following statement and justify your answer: If event A and event B are not mutually exclusive, neither are events A, B, and C for every event C.

> An experiment has 20 possible outcomes, all equally likely. An event can occur in five ways. The probability that the event occurs is ___.

> What does it mean for three events to be mutually exclusive?

> In a designed experiment, a. what are the experimental units? b. if the experimental units are humans, what term is often used in place of experimental unit?

> What does it mean for two events to be mutually exclusive?

> Consider the set consisting of the first 10 positive whole numbers (i.e., 1–10). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 6 b. at most 3 c. between 2 and 5, inclusive

> Iron is essential to most life forms and to normal human physiology. It is an integral part of many proteins and enzymes that maintain good health. Recommendations for iron are provided in Dietary Reference Intakes, developed by the Institute of Medicine

> Consider the set consisting of the first 12 positive whole numbers (i.e., 1–12). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. at least 9 b. at most 10 c. between 5 and 8, inclusive

> Construct a Venn diagram representing the event a. (A & (not B)). b. ((A or B) & (not (A & B)))

> Construct a Venn diagram representing the event a. (A or B or C). b. ((not A) & B).

> Construct a Venn diagram representing the event a. (A & B). b. (A & B & C).

> Construct a Venn diagram representing the event a. (not E). b. (A or B).