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statistics for experimentert
Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions
Russian Presidential Election. According to the Central Election Commission of the Russian Federation, a frequency distribution for the March 4, 2012 Russian presidential election is as follows.Candidate Votes Vladimir Putin 45,513,001 Gennady Zyuganov 12,288,624 Mikhail Prokhorov 5,680,558
Cardiovascular Hospitalizations. From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table showing the number of female hospitalizations for cardiovascular disease, by age group, during one year.Age group (yr) Number
Housing Units. 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.Rooms No. of units 1 601 2 1,404 3 11,433 4
Murder Victims. As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table.Age (yr) Frequency 20–24 2329 25–29 1892 30–34 1414 35–39 1046 40–44 900 45–49 854
The population of a certain country was studied in an article.The authors examined the different occupations for males and females in the country. The accompanying table is a frequency distribution of occupation type for males taking part in a survey.Occupation Frequency Administrative/M 2346
Nobel Laureates. From Wikipedia and the article “Which Country Has the Best Brains?” from BBC News Magazine, we obtained a frequency distribution of the number of Nobel Prize winners, by country.Country Winners United States 338 United Kingdom 119 Germany 103 France 59 Sweden 29 Switzerland 25
Graduate Science Students. According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows. Frequencies are in thousands. Note: Earth
Family Size. A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current Population Survey, published by the U.S. Census Bureau, the size distribution of U.S. families is as follows. Frequencies are in
Dice. Two balanced dice are rolled. Refer to Fig. 4.1 on page 181 and determine the probability that the sum of the dice isa. 6.b. even.c. 7 or 11.d. 2, 3, or 12.
Coin Tossing. A balanced dime is tossed three times. The possible outcomes can be represented as follows.HHH HTH THH TTH HHT HTT THT TTT Here, for example, HHT means that the first two tosses come up heads and the third tails. Find the probability thata. exactly two of the three tosses come up
Housing Units. Refer to Exercise 4.19.a. Which, if any, of the events in parts (a)–(e) are certain? impossible?b. Determine the probability of each event identified in part (a).
Family Size. Refer to Exercise 4.24.a. Which, if any, of the events in parts (a)–(e) are certain? impossible?b. Determine the probability of each event identified in part (a).
Gender and Handedness. This problem requires that you first obtain the gender and handedness of each student in your class. Subsequently, determine the probability that a randomly selected student in your class isa. female.b. left-handed.c. female and left-handed.d. neither female nor left-handed.
The probability that an individual amoeba will split to create two amoebas is 3/4, and the probability that it will die out without producing any offspring is 1/4. What is the probability that the family tree of the original amoeba will go on forever?
Women Governors. Suppose that 1414 of the 7070 state governors in a country were women. On each day of 2013, one of these state governors was randomly selected to read the invocation on a popular radio program. On approximately how many of those days should it be expected that a woman was chosen?A
Bilingual and Trilingual. At a certain university in the United States, 62% of the students are at least bilingual—speaking English and at least one other language. Of these students, 80% speak Spanish and, of the 80% who speak Spanish, 10% also speak French.Determine the probability that a
Consider the random experiment of tossing a coin once. There are two possible outcomes for this experiment, namely, a head (H) or a tail (T).a. Repeat the random experiment five times—that is, toss a coin five times—and record the information required in the following table.(The third and
Roulette. An American roulette wheel contains 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. For a bet on red, the house pays even odds (i.e., 1 to 1). What should the odds actually be to
Best Age. In a psychological survey about people’s perception of the best age to be, 2000 adults from various age groups were asked what they thought the best age to be was. With an average response of 25 years, around 54% of the people picked up the exact age of 35 as the best age. What are the
Belmont Stakes. The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and Revolutionary, for the 2013 Belmont Stakes were 7 to 2 (against) and 5 to 1 (against),
Cursing Your Computer. A study was conducted by the firm Coleman & Associates, Inc. to determine who curses at their computer. The results, which appeared in USA TODAY, indicated that 46% of people age 18–34 years have cursed at their computer. What are the odds against a randomly selected 18- to
Lightning Casualties. An issue of Travel + Leisure Golf magazine reported several facts about lightning. Here are three of them.The odds of an individual being struck by lightning in a year in the United States are about 280,000 to 1 (against). The odds of an individual being struck by lightning in
Construct a Venn diagram representing the eventa. (not E).b. (A or B).
Construct a Venn diagram representing the eventa. (A & B).b. (A & B & C).
Construct a Venn diagram representing the eventa. (A or B or C).b. ((not A) & B).
Construct a Venn diagram representing the eventa. (not (A & B)).b. (A or (not B)) & (not (A & B)).
Consider the set consisting of the first 20 positive whole numbers (i.e., 1−20). Determine explicitly the numbers in the set that satisfy each of the following conditions:a. at least 11b. at most 5c. between 14 and 19, inclusive
What does it mean for two events to be mutually exclusive?
What does it mean for three events to be mutually exclusive?
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.
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.
Draw a Venn diagram portraying four mutually exclusive events.Applying the Concepts and Skills
Dice. 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.
Colorful Candies. A single packet of candies contains 6 candy colors within it. The distribution of the colors in a packet of 100 candies is as given in the following table.Color Red Yellow Blue Brown Green Orange Number 14 14 18 12 18 24 List the outcomes constituting A = event that a
A committee consists of five executives, three women and two men. Their names are Sarah (S), Robert (R), Francisca (F), Gary (G), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws.The person getting the longest
Coin Tossing. When a dime is tossed four times, there are the following 16 possible outcomes.HHHH HTHH THHH TTHH HHHT HTHT THHT TTHT HHTH HTTH THTH TTTH HHTT HTTT THTT TTTT Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth
Refer to Exercise 4.53. List the outcomes that constitute each of the following events where A = event the die comes up even B = event the die comes up 5 or more C = event the die comes up at most 2a. (not A)b. (A & B)c. (B or C)
Horse Racing. Refer to Exercise 4.54. 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)
Committee Selection. Refer to Exercise 4.55. 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)
Coin Tossing. Refer to Exercise 4.56. 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)
The following frequency distribution provides a certain condition prevalence frequency distribution for 63 regions.Condition (%) Frequency 4–under 5 8 5–under 6 10 6–under 7 18 7–under 8 13 8–under 9 7 9–under 10 4 10–under 11 3 A = event that has a prevalence of at least 8%B = event
Water Consumption. In the 2008 report entitled “Water Poverty in Urban India: A Study of Major Cities” by Abdul Shaban, water consumption in domestic households of major Indian cities has been explored. Given below is the data collected from a few houses in New Delhi.Consumption in Liters
World Series. 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 World Series History on the
NBA Finals. 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 the number of series that were
The following table provides a frequency distribution for the number of rooms in this country’s housing units. The frequencies are in thousands.Rooms No. of units 1 570 2 1,424 3 10,949 4 23,362 5 27,938 6 24,609 7 14,668 8+ 17,211 A = event that the unit has at most 4 rooms B = event that the
Protecting the Environment. 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 Valley region. The
Dice. Refer to Exercise 4.53.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?
Colorful Candies. Each part of this exercise contains events from Exercise 4.54. In each case, decide whether the events are mutually exclusive.a. A and Bb. B and Cc. A, B, and Cd. A, B, and De. A, B, C, and D
Housing Units. Refer to Exercise 4.65. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive.
Protecting the Environment. Refer to Exercise 4.66. Among the events A, B, C, and D, identify the collections of events that are mutually exclusive.
Let A, B, and C be events of a sample space. Complete the following table.Event Description(A & B) Both A and B occur At least one of A and B occurs(A & (not B))Neither A nor B occur(A or B or C)All three of A, B, and C occur Exactly one of A, B, and C occurs Exactly two of A, B, and C occur At
Playing Cards. 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 event that a red card is
Poker Chips. 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 probability notation.
Suppose that A and B are events such that P(A) = 1/6, P(A or B) = 1/4, and P(A & B) = 1/15.a. Find P(B).b. Are events A and B mutually exclusive? Explain your answer.
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).Applying the Concepts and Skills
Ages of Senators. 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.Age (yr) No. of senators Under 50 11
Labor Force Participation. The Government of Sri Lanka issues a report every year on the basis of its labor force survey. These surveys are available on their official Website statistics.gov.lk. According to their annual report of 2013, the unemployment rate has decreased because of increase in the
Murder Weapons. The following probability model shows the distribution of murders by type of weapon for murder cases in a particular country over the past 12 years.Weapon Probability Gun 0.667 Knife 0.124 Blunt object 0.047 Personal weapon 0.065 Strangulation 0.016 Fire 0.007 Other 0.074 What is
Internet Access. 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.Household income Percentage
Religion in a country. According to a national survey in a certain country, the distribution of religious affiliation among adults in that country is as shown in the accompanying table.Affiliation Relative frequency Protestant 0.476 Catholic 0.235 Jewish 0.012 Mormon 0.024 Other 0.253 Find the
Ages of Senators. Refer to Exercise 4.87. Use the complementation rule to find the probability that a randomly selected U.S. senator isa. 50 years old or older.b. under 70 years old.
Sales Tax Receipts. Refer to Exercise 4.88. Use the complementation rule to find the probability that one of these Type 4A development corporations selected at random has receiptsa. of at least $25,000.b. less than $500,000.
Student Debt. The Association of American Universities published a report titled “Looking More Closely at Student Debt.” This report explores the issue about the cost of a college education and its impact on student loan debt. Using information from a credit reporting company, the following
Naturalization. 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.Age (yr) Frequency Age (yr) Frequency 18–19 5,958 45–49 42,820
Gender and Divorce. 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 = event the person is
School Enrollment. 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 attend public colleges. What
Smart Phones. A survey in a certain city revealed that people have smart phones of three major companies, Apple, HTC and Nokia. Circulation information indicates that 56.0% of people have Apple smartphones, 24.6% have HTC, 29.4% have Nokia, 5.9%have both Apple and Nokia, 9.8% have both Apple and
General Addition Rule Extended. The general addition rule for two events is presented in Formula 4.3 on page 197 and that for three events is displayed on page 199.a. Verify the general addition rule for three events.b. Write the general addition rule for four events and explain your reasoning.
Give an example ofa. univariate data.b. bivariate data.In each of Exercises 4.107–4.110,a. fill in the missing entries in the contingency table.b. determine P(C1), P(R2), and P(C1 & R2).c. construct the corresponding joint probability distribution.
New England Patriots. From the National Football League (NFL) Web site, in the New England Patriots Roster, we obtained information on the weights and years of experience for the players on that team, as of September 26, 2013. The following contingency table provides a cross-classification of those
Motor Vehicle Use. The Federal Highway Administration compiles information on motor vehicle use around the globe and publishes its findings in Highway Statistics. Following is a contingency table for the number of motor vehicles in use in North American countries, by country and type of vehicle,
Naval Classifications. The U.S. Department of Defense collects various data on military personnel. The following contingency table provides a joint frequency distribution for marital status and pay grade of active Naval military during one year. Pay grades are divided into three groups: Enlisted,
Farms. The U.S. Department of Agriculture publishes information about U.S. farms in Census of Agriculture. A joint frequency distribution for number of farms, by acreage and tenure of operator, is provided in the following contingency table. Frequencies are in thousands. Acreage Tenure of operator
Field Trips. P. Li et al. analyzed existing problems in teaching geography in rural counties in the article “Geography Education in Rural Tennessee Counties” (Geography, Vol. 88, No. 1, pp. 63–74).Fifty-one high-school teachers from the Upper Cumberland Region of Tennessee were surveyed. The
Fear of Gangs. In the article “Growing Pains and Fear of Gangs” (Applied Psychology in Criminal Justice, Vol. 5, No. 2, pp. 139–164), B. Brown and W. Benedict examined the relationship between worry about a gang attack and actually being a victim of a gang attack. Interviews of a sample of
New England Patriots. Refer to Exercise 4.111.a. For a randomly selected player on the New England Patriots, describe the events Y3, W2, and (W1 & Y2) in words.b. Compute the probability of each event in part (a). Interpret your answers in terms of percentages.c. Construct a joint probability
Motor Vehicle Use. Refer to Exercise 4.112.a. For a randomly selected vehicle, describe the events C1, V3, and (C1 & V3) in words.b. Compute the probability of each event in part (a).c. Compute P(C1 or V3), using the contingency table and the f/N rule.d. Compute P(C1 or V3), using the general
Naval Classifications. Refer to Exercise 4.113. An active Naval military personnel during the year in question is selected at random.a. Use the letters in the margins of the contingency table to represent each of the following three events: The person obtained is (i)single with children, (ii) a
Farms. Refer to Exercise 4.114. A U.S. farm is selected at random.a. Use the letters in the margins of the contingency table to represent each of the following three events: The farm obtained (i) has between 180 and 500 acres, (ii) is part-owner operated, and (iii) is full-owner operated and has at
What does the general addition rule (Formula 4.3 on page 197)mean in the context of the probabilities in a joint probability distribution?
In this exercise, you are asked to verify that the sum of the joint probabilities in a row or column of a joint probability distribution equals the marginal probability in that row or column. Consider the following joint probability distribution.C1 ··· Cn P(Ri)R1 P(R1 & C1) ··· P(R1 & Cn)
Give an example of the conditional probability of an event being the same as the unconditional probability of the event. (Hint: Consider the experiment of tossing a coin twice.)
Suppose that A and B are events such that P(A) = 2/11 and P(A & B) = 7/52. Determine P(B | A).In each of Exercises 4.130–4.133, we have presented either a contingency table or a joint probability distribution. In each case, determine both P(C1 | R2) and P(R2 | C1).4.130 C1 C2 Total R1 3 7 10 R2 8
Binary Digit. Any value entered in the computer is converted first to it binary equivalent. The four possible equally likely outcomes for a two binary digit are 00, 01, 10, 11. Let A = event the first digit is 1, B = event the second digit is 1, and C = event at least one digit is 1.Determine the
Playing Cards. One card is selected at random from an ordinary deck of 52 playing cards. Let A = event a face card is selected, B = event a king is selected, and C = event a heart is selected.Find the following probabilities and express your results in words.Compute the conditional probabilities
State Populations. From Infoplease, we obtained data on state population from which we constructed the following frequency distribution.Population size(millions) Frequency Under 1 6 1–under 2 8 2–under 3 6 3–under 5 8 5–under 10 15 10 & over 7 Compute the following conditional probabilities
Housing Units. A government bureau in a certain country publishes data on housing units in a survey. The accompanying table provides a frequency distribution for the number of rooms in housing units. The frequencies are in thousands. Consider a housing unit selected at random. Compute the following
Unemployment. In the Sri Lankan Government’s 2013 Labor Force Survey report, found on statistics.gov.lk, the percentage distribution of economically inactive population in Sri Lanka has been discussed. The following contingency table cross-classifies a sample of 129.5% economically inactive Sri
New England Patriots. From the National Football League(NFL) Web site, in the New England Patriots Roster, we obtained information on the weights and years of experience for the players on that team, as of September 26, 2013. The following contingency table provides a cross-classification of those
Acclaim or Attack. In the article “A Functional Analysis Comparison of Web-Only Advertisements and Traditional Television Advertisements from the 2004 and 2008 Presidential Campaigns”(Journalism & Mass Communication Quarterly, Vol. 90, No. 1, pp. 23–38), author C. Roberts explores whether a
Self-Concept and Sightedness. Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article ‘‘An Exploration into Self Concept: A Comparative Analysis between the
Living Arrangements. As reported by the U.S. Census Bureau in America’s Families and Living Arrangements, the living arrangements by age of U.S. citizens 15 years of age and older are as shown in the following joint probability distribution. Age (yr)Living arrangement Alone With spouse With
Smartphone Ownership. From the document Smartphone Ownership by the Pew Research Center and the document Current Population Survey by the U.S. Census Bureau, we constructed the following joint probability distribution for educational attainment and smartphone ownership for U.S. adults. Education
HPV Vaccine. In the article “Correlates for Completion of 3-dose Regimen of HPV Vaccine in Female Members of a Managed Care Organization” (Mayo Clinical Proceedings, Vol. 84. pp. 864–870), C. Chao et al. examined characteristics that may influence whether young female patients complete a
Dentist Visits. The National Center for Health Statistics publishes information about visits to the dentist in National Health Interview Survey. Here is a joint probability distribution for the length of time (in years) since last visit to a dentist or other dental health professional, by age, for
Scientists and Engineers. The U.S. National Science Foundation collects data on science and engineering (S&E) degrees awarded and publishes the results in Science and Engineering Degrees. During one year, 75.2% of S&E degrees awarded were for Bachelor’s degrees and 37.8% of S&E degrees were
S&E Degrees. A national science foundation in a certain country collects data on science and engineering (S&E) degrees awarded and publishes the results in a journal. During one year, 77.4% of S&E degrees awarded were for Bachelor’s degrees and 35.7% of S&E degrees were Bachelor’s degrees
National Guard. The U.S. Department of Defense collects data on active members in the National Guard. Results are published in Selected Manpower Statistics. According to that document, 77.0%of members are in the Army National Guard and 10.2% of members are Black and in the Army National Guard. What
Physician Characteristics. The Association of American Medical Colleges (AAMC) compiles data on active U.S. physicians and publishes its results in the Physician Specialty Data Book.From that document, 13.6% of active U.S. physicians specialize in internal medicine and 8.67% of active U.S.
Dice. Three balanced dice are thrown. What is the probability that one die comes up with 1, given that thea. remaining two dice come up 3 and 5?b. sum of the dice is 7?c. sum of the dice is 15?
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