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Introductory Statistics 10th Edition Neil A. Weiss - Solutions

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, Officer, and Warrant
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.a. Fill in the six missing
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 following
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 high school students
Refer to Exercise 4.111.In E 4.111From 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
Use. Refer to Exercise 4.112.In E 4.112The 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
Refer to Exercise 4.113. An active Naval military personnel during the year in question is selected at random.In E 4.113The 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
Refer to Table 4.1 on page 157. a. List the possible samples without replacement of size 3 that can be obtained from the population of five officials. If a simple random sample without replacement of three officials is taken from the five officials, determine the probability that b. The governor,
Refer to Exercise 4.114. A U.S. farm is selected at random.In E 4.114a. 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, (iii) Is full-owner operated and has
Explain why the joint events in a contingency table are mutually exclusive.
What does the general addition rule (Formula 4.3 on page 175) mean in the context of the probabilities in a joint probability distribution? In Formula 4.3 If A and B are any two events, then P(A or B) = P(A) + P(B) − P(A & B).
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.a. Explain why R1 = (R1 & C1) or
Regarding conditional probability: a. What is it? b. Which event is the "given event"?
Give an example of the conditional probability of an event being the same as the unconditional probability of the event.
Suppose that A and B are events such that P(A) = 0.75 and P(A & B) = 0.25. Determine P(B | A).
Suppose that C and D are events such that P(C) = 0.5 and P(C & D) = 0.2. Determine P(D | C).
Suppose that C and D are events such that P(C) = 4/5 and P(C & D) = 3/10. Find P(D | C).
Suppose that A and B are events such that P(A) = 2/7 and P(A & B) = 3/25. Determine P(B | A).
Refer to Table 4.1 on page 157. a. List the possible samples without replacement of size 4 that can be obtained from the population of five officials. If a simple random sample without replacement of four officials is taken from the five officials, determine the probability that b. The governor,
We have presented either a contingency table or a joint probability distribution. In each case, determine both P(C1 | R2) and P(R2 | C1).
A balanced dime is tossed twice. The four possible equally likely outcomes are HH, HT, TH, TT. Let A = event the first toss is heads, B = event the second toss is heads, and C = event at least one toss is heads. Determine the following probabilities and express your results in words. Compute the
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 directly; do
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
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
In the article "Judicial Dispositions of Ex-Parte and Domestic Violence Protection Order Hearings: A Comparative Analysis of Victim Requests and Court Authorized Relief" (Journal of Family Violence, Vol. 20, No. 3, pp. 161-170), D. Year wood looked at the discrepancies between what a victim of
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 data.Compute the
In the article "A Functional Analysis Comparison ofWeb-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 difference exists in
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 Adolescents Who Are Sighted and Blind
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.A U.S. citizen 15 years of age or older is selected at random. Determine the
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.A U.S. adult is selected at random.
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 three-injection
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 U.S. adults
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 Bachelor's degrees awarded to
As reported by the Federal Bureau of Investigation in Crime in the United States, 5.1% of property crimes are committed in rural areas and 1.6% of property crimes are burglaries committed in rural areas. What percentage of property crimes committed in rural areas are burglaries?
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 percentage of
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. physicians are under age 55 and
Two balanced dice are thrown, one red and one black. What is the probability that the red die comes up 1, given that the a. Black die comes up 3? b. Sum of the dice is 4? c. Sum of the dice is 9?
A king and queen have two children. Assuming that a child of the king and queen is equally likely to be a boy or a girl, what is the probability that both children are boys, given that a. The first child born is a boy? b. At least one child is a boy?
Refer to Exercise 4.139.In E 4.139a. Construct a joint probability distribution. b. Determine the probability distribution of weight for rookies; that is, construct a table showing the conditional probabilities that a rookie weighs under 200 pounds, between 200 and 300 pounds, and over 300
Let A and B be events, each with positive probability.a. State in words what it means for event B to be positively correlated with event A; negatively correlated with event A; independent of event A.b. Show that event B is positively correlated with event A if and only if event A is positively
Suppose that it has been determined that "one-fourth of drivers at fault in a car accident use a certain drug."a. Explain in words what it means to say that being the driver at fault in a car accident is positively correlated with use of the drug.b. Under what condition on the percentage of drivers
Regarding the general multiplication rule and the conditional probability rule: a. State these two rules. b. Explain the relationship between them. c. Why are two different variations of essentially the same rule emphasized?
Suppose that A and B are two events. a. What does it mean for event B to be independent of event A? b. If event A and event B are independent, how can their joint probability be obtained from their marginal probabilities?
Suppose P(C) = 1/4 and P(D |C) = 4/5. Find P(C & D).
Preeclampsia is a medical condition characterized by high blood pressure and protein in the urine of a pregnant woman. It is a serious condition that can be life threatening to the mother and child. In the article "Women's Experiences of Preeclampsia: Australian Action on Preeclampsia Survey of
Suppose P(A) = 7/8 and P(B | A) = 5/7. Find P(A& B).
Suppose that C and D are independent events such that P(C) = 0.7 and P(D) = 0.6. Find P(C&D).
Suppose that A and B are independent events such that P(A) = 0.3 and P(B) = 0.2. Find P(A& B).
Suppose that A and B are independent events such that P(A) = 5/8 and P(B) = 4/7. Find P(A& B).
Suppose that C and D are independent events such that P(C) = 3/4 and P(D) = 2/5. Find P(C & D).
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
Suppose that A, B, and C are independent events such that P(A) = 0.8, P(B) = 0.5, and P(C) = 0.3. Find P(A& B &C).
Suppose that C, D, and E are independent events such that P(C) = 7/8, P(D) = 5/7, and P(E) = 2/3. Find P(C & D & E).
According to the Opinion Research Corporation, 44% of U.S. women suffer from holiday depression, and, from the U.S. Census Bureau's Current Population Reports, 52% of U.S. adults are women. Find the probability that a randomly selected U.S. adult is a woman who suffers from holiday depression.
The report "Addiction Medicine: Closing the Gap between Science and Practice" from the National Center on Addiction and Substance Abuse at Columbia University reveals that addiction treatment is neglected by the medical system in the United States. It shows, in particular, that 16% of Americans
A person has agreed to participate in an extrasensory perception (ESP) experiment. He is asked to randomly pick two numbers between 1 and 6. The second number must be different from the first. Let H = event the first number picked is a 3, and K = event the second number picked exceeds
Cards numbered 1, 2, 3, . . . , 10 are placed in a box. The box is shaken, and a blindfolded person selects two successive cards without replacement. a. What is the probability that the first card selected is numbered 6? b. Given that the first card is numbered 6, what is the probability that the
A frequency distribution for the class level of students in Professor Weiss's introductory statistics course is as follows.Class __________________ FrequencyFreshman ........................... 6Sophomore .........................15Junior ...............................12Senior
The National Governors Association publishes data on U.S. governors in Governors' Political Affiliations & Terms of Office. Based on that document, we obtained the following frequency distribution for U.S. governors, as of 2013.Party ______________ FrequencyDemocratic
The Association of American Medical Colleges (AAMC) compiles data on medical school faculty and publishes the results in AAMC Faculty Roster. The following contingency table cross-classifies medical school faculty by the characteristics gender and rank.a. Find P(R3). b. Find P(R3 | G1). c. Are
The National Center for Health Statistics compiles data on injuries and publishes the information in Vital and Health Statistics. A contingency table for injuries in the United States, by circumstance and gender, is as follows. Frequencies are in millions.a. Find P(C1).b. Find P(C1 | S2).c. Are
The U.S. Congress, Joint Committee on Printing, provides information on the composition of Congress in Congressional Directory. Here is a joint probability distribution for the members of the 113th Congress by legislative group and political party. The "other" category includes Independents and
The U.S. National Science Foundation publishes data on doctoral degrees conferred in the document Science and Engineering Doctorate Awards. The following joint probability distribution summarizes the doctoral degrees conferred in the social sciences and psychology by gender during one year.a. Find
When a balanced dime is tossed three times, eight equally likely outcomes are possible: HHH ...... HTH ......THH ......TTH HHT ....... HTT ......THT .......TTT Let A = event the first toss is heads, B = event the third toss is tails, and C = event the total number of heads is 1. a. Compute P(A),
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 units1
When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 159. Let A = event the red die comes up even, B = event the black die comes up odd, C = event the sum of the dice is 10, and D = event the sum of the dice is even. a. Compute P(A), P(B),
Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are aces if a. The first card is replaced before the second card is drawn. b. The first card is not replaced before the second card is drawn.
In the game of Yahtzee, five balanced dice are rolled. a. What is the probability of rolling all 2s? b. What is the probability that all the dice come up the same number?
In a letter to the editor that appeared in the February 23, 1987, issue of U.S. News and World Report, a reader discussed the issue of space shuttle safety. Each "criticality 1" item must have 99.99% reliability, according to NASA standards, meaning that the probability of failure for such an item
It is not uncommon after a round of golf to find a foursome in the clubhouse shaking the bar dice to see who buys the refreshments. In the first two rounds, each person gets to shake the five dice once. The person with the most dice with the highest number is eliminated from the competition to see
According to Accident Facts, published by the National Safety Council, a probability distribution of age group for drivers at fault in fatal crashes is as follows. Age (yr) ____________________ Probability 16-24 .............................. 0.255 25-34 .............................. 0.238 35-64
One of the more contentious issues is whether there should be the death penalty for a person convicted of murder. According to estimates by Gallup, the percentages of U.S. adults that approve of, disapprove of, and have no opinion about the death penalty are 61%, 35%, and 4%, respectively. Suppose
A hardware manufacturer produces nuts and bolts. Each bolt produced is attached to a nut to make a single unit. It is known that 2% of the nuts produced and 3% of the bolts produced are defective in some way. A nut-bolt unit is considered defective if either the nut or the bolt has a defect. a.
The National Center for Health Statistics compiles information on activity limitations. Results are published in Vital and Health Statistics. The data show that 13.6% of males and 14.4% of females have an activity limitation. Are gender and activity limitation statistically independent? Explain
Marilyn vos Savant writes the column "Ask Marilyn," which appears in Parade Magazine. One reader submitted the following question: My daughter is one of five finalists for a grant that awards two scholarships and is also one of five finalists for a separate grant that awards one scholarship. All
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
For three events, say, A, B, and C, the general multiplication rule is P(A & B & C) = P(A) · P(B | A) · P(C | (A & B)). a. Suppose that three cards are randomly selected without replacement from an ordinary deck of 52 cards. Find the probability that all three cards are hearts; the first two
Students are given three chances to pass a basic skills exam for permission to enroll in Calculus I. Sixty percent of the students pass on the first try; of those that fail on the first try, 54% pass on the second try; and of those remaining, 48% pass on the third try. a. What is the probability
In this exercise, you examine further the concepts of independent events and mutually exclusive events.a. If two events are mutually exclusive, determine their joint probability.b. If two nonimpossible (i.e., positive probability) events are independent, explain why their joint probability is not
Three events A, B, and C are said to be independent ifP(A & B) = P(A) · P(B),P(A & C) = P(A) · P(C),P(B & C) = P(B) · P(C), andP(A & B & C) = P(A) · P(B) · P(C).What is required for four events to be independent? Explain your definition in words.
When two balanced dice are rolled, 36 equally likely outcomes are possible, as illustrated in Fig. 4.1 on page 159. LetIn Fig 4.1A = event the red die comes up even, B = event the black die comes up even, C = event the sum of the dice is even, D = event the red die comes up 1, 2, or 3, E = event
When a balanced coin is tossed four times, 16 equally likely outcomes are possible, as shown in the following table.Let A = event the first toss is heads, B = event the second toss is tails, and C = event the last two tosses are heads. Apply the definition of independence for three events stated in
Are exhaustive events necessarily mutually exclusive? Are mutually exclusive events necessarily exhaustive? Explain your answers.
Explain why an event and its complement are always mutually exclusive and exhaustive.
The events A1, A2, . . . are mutually exclusive and exhaustive. We have provided P(A1), P(A2), . . . and P(B | A1), P(B | A2), . . . . In each case,a. Use the rule of total probability to find P(B).b. Apply Bayes's rule to find P(A1 | B).
From the National Golf Foundation and the U.S. Census Bureau, we obtained the following statistics for Americans: 15.1% of males and 4.3% of females play golf, respectively; 49.2% and 50.8% of the population are male and female, respectively. Find the probability that a randomly selected Americana.
According to an Opinion Dynamics Poll published in USA TODAY, roughly 54% of U.S. men and 33% of U.S. women believe in extraterrestrial aliens. Of U.S. adults, roughly 48% are men and 52% women. a. What percentage of U.S. adults believe in such aliens? b. What percentage of U.S. women believe in
A moviegoer is defined as a person who goes to the movies at least once a month. From the article Hollywood Demographics on the Indiewire website, we obtained the following data on moviegoers in the United States and Canada. The first two columns provide an age distribution; the third column gives
The following table provides statistics found in the document Science and Engineering Indicators, issued by the National Science Foundation, for a sample of 1564 adults. The first two columns of the table present an educational level distribution for the adults; the third column gives the
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
The aim of a study in the article, "Separate and Joint Effects of Physical and Mental Health on Participation of People with Somatic Chronic Illness" (Journal of Nursing and Healthcare of Chronic Illness, Vol. 3, Issue 1, pp. 61- 72), by D. Jansen and M. Rijken, is to examine the extent to which
A person is said to be overweight if his or her body mass index (BMI) is between 25 and 29, inclusive; a person is said to be obese if his or her BMI is 30 or greater. From the document Utah Behavioral Risk Factor Surveillance System (BRFSS) Local Health District Report, issued by the Utah
Based on research by the Associated Press and the National Constitution Center 85% of Democrats, 81% of Republicans, and 78% of Independents support limiting corporate influence in political elections. Estimates from Gallup show that 32% of U.S. adults are Democrats, 28% are Republicans, and 40%
Textbook publishers must estimate the sales of new (first-edition) books. The records of one major publishing company indicate that 10% of all new books sell more than projected, 30% sell close to the number projected, and 60% sell less than projected. Of those that sell more than projected, 70%
At a grocery store, eggs come in cartons that hold a dozen eggs. Experience indicates that 78.5% of the cartons have no broken eggs, 19.2% have one broken egg, 2.2% have two broken eggs, and 0.1% have three broken eggs, and that the percentage of cartons with four or more broken eggs is negligible.
Medical tests are frequently used to decide whether a person has a particular illness. The sensitivity of a test is the probability that a person having the illness will test positive; the specificity of a test is the probability that a person not having the illness will test negative. According to
Several years ago, in a column published by Marilyn vos Savant in Parade Magazine, an interesting probability problem was posed. That problem is now referred to as the Monty Hall Problem because of its origins from the television show Let's Make a Deal. Following is a version of the Monty Hall
You have two cards. One is red on both sides, and the other is red on one side and black on the other. After shuffling the cards behind your back, you select one of them at random and place it on your desk with your hand covering it. Upon lifting your hand, you observe that the face showing is
Refer to Example 4.26 on page 205. a. Determine the probability that a randomly selected nonsmoker has lung disease. b. Use the probability obtained in part (a) and the result of Example 4.26 to compare the rates of lung disease for smokers and nonsmokers.
What are counting rules? Why are they important?

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