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statistics for experimentert

Introductory Statistics 10th Global Edition Neil A. Weiss - Solutions

Colorful Candies. A single packet of candies contains 100 candies of 4 colors each, yellow, blue, red and green, all in equal numbers. Assuming that 1 candy is picked at a time and the first picked is red, what is the probability that the second candy is (without replacement)a. blueb. red Extending
New England Patriots. Refer to Exercise 4.139.a. 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
Drugs and Car Accidents. 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
Suppose P(A) = 0.6 and P(B | A) = 0.4. Find P(A & B).
Suppose P(C) = 0.3 and P(D |C) = 0.8. Find P(C & D).
Suppose P(C) = 1/4 and P(D |C) = 4/5. Find P(C & D).
Suppose P(A) = 7/8 and P(B | A) = 5/7. Find P(A & B).
Suppose that A, B, and C are independent events such that P(A) = 0.9, P(B) = 0.3, and P(C) = 0.7. Find P(A & B & C).
Suppose that C, D, and E are independent events such that P(C) = 3/7, P(D) = 5/11, and P(E) = 5/7. Find P(C & D & E).Applying the Concepts and Skills
Holiday Depression. 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
Addiction Medicine. 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,
ESP experiment. A person has agreed to participate in an extrasensory perception (ESP) experiment. He is asked to randomly pick two numbers between 0 and 9, inclusive. The second number must be different from the first. Let H = event the first number is 5, and K = event the second number picked
Colorful Candies. A single packet of candies contains 100 candies of 4 colors each, yellow, blue, red and green, all equal in number. A blindfolded person selects two successive candies without replacement.a. What is the probability that the first candy selected is blue?b. Given that the first
Class Levels. A frequency distribution for the class level of students in Professor Weiss’s introductory statistics course is as follows.Class Frequency Freshman 6 Sophomore 15 Junior 12 Senior 7 Two students are randomly selected without replacement. Determine the probability thata. the first
Gender. The Indian Ministry of Labor & Employment publishes data on the national employment-unemployment scenario among different social groups. Based on that document for 2013−2014, we obtained the following frequency distribution (expressed as rounded off percentages) for gender in urban
Medical School Faculty. 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. Rank Gender Male
Injured Americans. 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. Gender Circumstance
U.S. Congress. 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
Doctoral Degrees. 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
Coin Tossing. 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), P(B), and P(C).b. Compute P(B
Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 171. 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),
Drawing Cards. Two cards are drawn at random from an ordinary deck of 52 cards. Determine the probability that both cards are hearts ifa. the first card is replaced before the second card is drawn.b. the first card is not replaced before the second card is drawn.
Yahtzee. 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?
Space Shuttle. A space shuttle is made up of 775 “criticality 1” items. Each “criticality 1” item must have 99.99% reliability, according to standards, meaning that the probability of failure for such an item is 0.0001. Determine the probability thata. none of the “criticality 1” items
Traffic Fatalities. 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 0.393 65 & over 0.114 Of three fatal automobile crashes,
Tires. A tire manufacturer produces tires and tubes. Each tube produced fits into a tire to make a single unit. It is known that 1.5% of the tires produced and 3.7% of the tubes produced are defective in some way. A tire-tube unit is considered defective if either the tire or the tube has a
Activity Limitations. 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
Scholarships. 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
General Multiplication Rule Extended. 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
Gender of Students. In Example 4.21 on page 216, we discussed randomly selecting, without replacement, two students from Professor Weiss’s introductory statistics class. Suppose now that three students are selected without replacement. What is the probability that the first two students chosen
Calculus Pretest. 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
Independence Extended. Three events A, B, and C are said to be independent if P(A & B) = P(A) · P(B), P(A & C) = P(A) · P(C), P(B & C) = P(B) · P(C), and P(A & B & C) = P(A) · P(B) · P(C).What is required for four events to be independent? Explain your definition in words.
Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as illustrated in Fig. 4.1 on page 181. Let A = 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 the
Binary Digits. According to the binary system, a 4-digit combination has 16 possible arrangements of the digits, as shown in the following table.0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Let A = event the first digit is 1, B = event the second digit is 0, and C
U.S. Demographics. Refer to Example 4.24 on pages 224–225. In probability notation, the percentage of Midwest residents can be expressed as P(R2). Do the same for the percentage ofa. Southern residents.b. Southern residents who are seniors.c. seniors who are Southern residents.Applying the
Women. From a report on world statistics, we obtained the following data for women: 15% of the population of high-income countries is females; out of which 30% are above the age of 60+;47% of population of middle-income countries is females; out of which 48% are above 60+. Find the probability that
Smoking. According to a certain global health risks report, roughly, 43% of men and 10% of women of the world population are smokers, and roughly 50.40% are men and 49.60%women.a. What percentage of world population are smokers?b. What percentage of women are smokers?c. What percentage of world
Moviegoers. 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
Education and Astrology. 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 educationallevel distribution for the adults; the third
Chronic Illness and Participation. 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.
Obesity and Age. 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
World Deaths. According to a certain global health risks report, 3.8% of the total number of deaths in the world can be attributed to childhood underweight in children, and 2.1% to suboptimal breastfeeding of newborns. Estimates show that 3.7% of these deaths are of males who die because of
Textbook Revision. 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
Decorative Candles. At a mart, decorative candles come in cartons that hold half a dozen candles. Experience indicates that 80% of the cartons have no damaged candles, 17.7% have one damaged candle, 2.2% have two damaged candles, and 0.1% have three damaged candles, and the percentage of cartons
Game Show. On a game show, there are three doors, behind each of which is one prize. Two of the prizes are worthless and one is valuable. A contestant selects one of the doors, following which, the game-show host, who knows where the valuable prize lies, opens one of the remaining two doors to
Red and Black. 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
Smoking and Lung Disease. Refer to Example 4.26 on page 227.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
Answer the following questions regarding permutations and combinations.a. What is a permutation?b. What is a combination?c. What is the major distinction between the two?
Determine the value of each quantity.a. 4C3b. 15C4c. 6C2d. 10C0e. 8C8
Fill in the blank: The number of possible permutations of m objects among themselves is .
Fill in the blank: The number of possible samples of size n from a population of size N is .
How many possible samples of size 5 are possible from a population of size 70?Applying the Concepts and Skills
Home Models and Elevations. Refer to Example 4.27 on pages 230–231. Suppose that the developer discontinues the Shalimar model but provides an additional elevation choice, D, for each of the remaining three model choices.a. Draw a tree diagram similar to the one shown in Fig. 4.28 depicting the
Home Models and Elevations. Refer to Example 4.27 on pages 230–231. Suppose that the developer provides an additional model choice, called the Nanaimo.a. Draw a tree diagram similar to the one shown in Fig. 4.28 depicting the possible choices for the selection of a home, including both model and
Tesla Model S. There are many choices to make when buying a new car. The options for a Tesla Model S can be found on the Tesla Motors website. For 2013, choices are available, among others, for roof (3), exterior color (9), seat fabric/color (4), interior trim (5), and wheels (5). How many
Roll Number. A particular institute assigns an 8-digit roll number to any enrolled student. The 8 digit roll number is divided into 2 sections: the first one consisting of three digits, out of which, the first two digits refer to the year in which the student has joined and last digit refers to the
Colorful Candies. A single packet of candies contains 100 candies of 6 colors each, yellow, blue, orange, green, red and brown.There are 24 orange candies, 18 green candies, 12 brown candies, 18 blue candies, 14 red candies, and 14 yellow candies. A blind-folded person is asked to pick 3 candies
Telephone Numbers. In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit local number. Suppose neither the first digit of an area code nor the first digit of a local number can be a zero but that all other choices are acceptable.a. How many different
Mutual Fund Investing. Investment firms usually have a large selection of mutual funds from which an investor can choose.One such firm has 25 mutual funds. Suppose that you plan to invest in five of these mutual funds, one during each quarter of coming years.In how many different ways can you make
Testing for ESP. An extrasensory perception (ESP) experiment is conducted by a psychologist. For part of the experiment, the psychologist takes 10 cards numbered 1–10 and shuffles them. Then she looks at the cards one at a time. While she looks at each card, the subject writes down the number he
Los Angeles Dodgers. From the official website of the 2013 Los Angeles Dodgers major league baseball team, we found that there were five active players on roster available to play outfield. Assuming that these five players could play any outfield position, how many possible assignments could
A Movie Festival. At a movie festival, a team of judges is to pick the first, second, and third place winners from the 27 films entered. How many possibilities are there?
Assigning Lease Properties. The Government of India has to allot ten properties on lease to seven different applicants. How many possibilities are there for the allotments?
Five-Card Stud. A hand of five-card stud poker consists of an ordered arrangement of five cards from an ordinary deck of 52 playing cards.a. How many five-card stud poker hands are possible?b. How many different hands consisting of three kings and two queens are possible?c. The hand in part (b) is
IRS Audits. The Internal Revenue Service (IRS) decides that it will audit the returns of 3 people from a group of 18. Use combination notation to express the number of possibilities and then evaluate that expression.
A Lottery. At a lottery, 100 tickets were sold and three prizes are to be given. How many possible outcomes are there ifa. the three prizes are equivalent?b. there is a first, second, and third prize?
Shake. Ten people attend a party. If each pair of people shakes hands, how many handshakes will occur?
Championship Series. Professional sports leagues commonly end their seasons with a championship series between two teams. The series ends when one team has won four games and so must last at least four games and at most seven games. How many different sequences of game winners are there in which
Five-Card Draw. A hand of five-card draw poker consists of an unordered arrangement of five cards from an ordinary deck of 52 playing cards.a. How many five-card draw poker hands are possible?b. How many different hands consisting of three kings and two queens are possible?c. The hand in part (b)
Senate Committees. The U.S. Senate consists of 100 senators, 2 from each state. A committee consisting of 5 senators is to be formed.a. How many different committees are possible?b. How many are possible if no state may have more than 1 senator on the committee?c. If the committee is selected at
Venus Throw. The Dr. Fisher’s Casebook feature “Codex magistri Piscatori,” appearing in an issue of Significance Magazine(Vol. 10, Issue 2, p. 28), showed an image, including the probability, of a “Venus throw,” one in which the outcome of tossing four balanced dice results in four
Which Key? Suppose that you have a key ring with eight keys on it, one of which is your house key. Further suppose that you get home after dark and can’t see the keys on the key ring. You randomly try one key at a time, being careful not to mix the keys that you’ve already tried with the ones
Quality Assurance. Refer to Example 4.36, which starts on page 236. Determine the probability that the number of defective TVs obtained by the engineer isa. exactly one.b. at most one.c. at least one.
The Birthday Problem. A biology class has 38 students.Find the probability that at least 2 students in the class have the same birthday. For simplicity, assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First, determine the probability
True-False Tests. A student takes a true-false test consisting of 10 questions. Assume that the student guesses at each question and find the probability thata. the student gets at least 5 questions correct.b. the student gets a 60% or better on the exam.Extending the Concepts and Skills
Florida Battleground State. From the Washington Post website, we found final results of the 2012 presidential election.According to that site, Barack Obama received about 50% of the popular vote in the battleground state of Florida. Suppose that 10 Floridians who voted in 2012 are selected at
Sampling Without Replacement. A simple random sample of size n is to be taken without replacement from a population of size N.a. Determine the probability that any particular sample of size n is the one selected.b. Determine the probability that any specified member of the population is included in
The Birthday Problem. Refer to Exercise 4.266, but now assume that the class consists of N students.a. Determine the probability that at least 2 of the students have the same birthday.b. If you have access to a computer or a programmable calculator, use it and your answer from part (a) to construct
use and understand the formulas in this chapter.
compute probabilities for experiments having equally likely outcomes.
interpret probabilities, using the frequentist interpretation of probability.
state and understand the basic properties of probability.
construct and interpret Venn diagrams.
find and describe (not E), (A & B), and (A or B).
determine whether two or more events are mutually exclusive.
understand and use probability notation.
state and apply the special addition rule.
state and apply the complementation rule.
state and apply the general addition rule.
read and interpret contingency tables.
construct a joint probability distribution.
compute conditional probabilities both directly and by using the conditional probability rule.
state and apply the general multiplication rule.
state and apply the special multiplication rule.
determine whether two events are independent.
understand the difference between mutually exclusive events and independent events.
determine whether two or more events are exhaustive.
state and apply the rule of total probability.
state and apply Bayes’s rule.
state and apply the basic counting rule (BCR).

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