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elementary statistics
Elementary Statistics 9th Edition Mario F. Triola - Solutions
For a standard normal distribution, find the percentage of data that area. within 1 standard deviation of the mean.b. within 1.96 standard deviations of the mean.c. between m 2 3s and m 1 3s.d. between 1 standard deviation below the mean and 2 standard deviations above the mean.e. more than 2
If 3.0% of the thermometers are rejected because they have readings that are too high and another 3.0% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others.5-2 Beyond the Basics
If 5% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
Find P90, the 90th percentile. This is the temperature reading separating the bottom 90% from the top 10%.
Deaths Currently, an average of 7 residents of the village of Westport (population 760) die each year (based on data from the U.S. National Center for Health Statistics).a. Find the mean number of deaths per day.b. Find the probability that on a given day, there are no deaths.c. Find the
Reasons for Being Fired Inability to get along with others is the reason cited in 17%of worker firings (based on data from Robert Half International, Inc.). Concerned about her company’s working conditions, the personnel manager at the Boston Finance Company plans to investigate the five employee
Employee Drug Testing Among companies doing highway or bridge construction, 80% test employees for substance abuse (based on data from the Construction Financial Management Association). A study involves the random selection of 10 such companies.a. Find the probability that 5 of the 10 companies
TV Ratings The television show West Wing has a 15 share, meaning that while it is being broadcast, 15% of the TV sets in use are tuned to West Wing (based on data from Nielsen Media Research). A special focus group consists of 20 randomly selected households (each with one TV set in use during the
a. What is a random variable?b. What is a probability distribution?c. A graph in USA Today listed the percentages for the number of days in a week that American adults cook at home in an average week. For example, 13% of American adults cook at home 3 days in an average week. The accompanying table
Poisson Approximation to Binomial For a binomial distribution with n 5 10 and p 5 0.5, we should not use the Poisson approximation because both of the conditions n 100 and np # 10 are not satisfied. Suppose we go way out on a limb and use the Poisson approximation anyway. Are the resulting
Poisson Approximation to Binomial The Poisson distribution can be used to approximate a binomial distribution if n 100 and np # 10. Assume that we have a binomial distribution with n 5 100 and p 5 0.1. It is impossible to get 101 successes in such a binomial distribution, but we can compute the
Earthquakes For a recent period of 100 years, there were 93 major earthquakes (at least 6.0 on the Richter scale) in the world (based on data from the World Almanac and Book of Facts). Assuming that the Poisson distribution is a suitable model, find the mean number of major earthquakes per year,
Roulette Scott bets on the number 7 for each of 200 spins of a roulette wheel. Because P(7) 5 1 38, he expects to win about 5 times.a. Find the probability of no wins in the 200 spins.b. Find the probability of at least one win in the 200 spins.c. Scott will lose money if the number of wins is 0,
Homicide Deaths In one year, there were 116 homicide deaths in Richmond, Virginia(based on “A Classroom Note on the Poisson Distribution: A Model for Homicidal Deaths in Richmond, VA for 1991,” in Mathematics and Computer Education, by Winston A. Richards). For a randomly selected day, find the
Deaths from Horse Kicks A classic example of the Poisson distribution involves the number of deaths caused by horse kicks of men in the Prussian Army between 1875 and 1894. Data for 14 corps were combined for the 20-year period, and the 280 corpsyears included a total of 196 deaths. After finding
Births Currently, 11 babies are born in the village of Westport (population 760) each year (based on data from the U.S. National Center for Health Statistics).a. Find the mean number of births per day.b. Find the probability that on a given day, there are no births.c. Find the probability that on a
Radioactive Decay Radioactive atoms are unstable because they have too much energy. When they release their extra energy, they are said to decay. When studying cesium 137, it is found that during the course of decay over 365 days, 1,000,000 radioactive atoms are reduced to 977,287 radioactive
Acceptable Defective Products Mario’s Pizza Parlor has just opened. Due to a lack of employee training, there is only an 0.8 probability that a pizza will be edible. An order for five pizzas has just been placed. What is the minimum number of pizzas that must be made in order to be at least 99%
Using the Empirical Rule and Chebyshev’s Theorem An experiment is designed to test the effectiveness of the MicroSort method of gender selection, and 100 couples try to have baby girls using the MicroSort method. In an example included in this section, the range rule of thumb was used to conclude
Car Crashes For drivers in the 20–24 age bracket, there is a 34% rate of car accidents in one year (based on data from the National Safety Council). An insurance investigator finds that in a group of 500 randomly selected drivers aged 20–24 living in New York City, 42% had accidents in the last
Opinions About Cloning A recent Gallup poll consisted of 1012 randomly selected adults who were asked whether “cloning of humans should or should not be allowed.”Results showed that 89% of those surveyed indicated that cloning should not be allowed.a. Among the 1012 adults surveyed, how many
Cholesterol Reducing Drug In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10 mg Atorvastatin tablets.That group contains 19 patients who experienced flu symptoms (based on data from Pfizer, Inc.). The probability of flu symptoms for a
Cell Phones and Brain Cancer In a study of 420,000 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. If we assume that such cancer is not affected by cell phones, the probability of a person having such a cancer is 0.000340.a. Assuming that cell
Are 10% of M&M Candies Blue? Mars, Inc., claims that 10% of its M&M plain candies are blue, and a sample of 100 such candies is randomly selected.a. Find the mean and standard deviation for the number of blue candies in such groups of 100.b. Data Set 19 in Appendix B consists of a random sample of
Determining Whether Complaints Are Lower After a Training Program The Newtower Department Store has experienced a 3.2% rate of customer complaints and attempts to lower this rate with an employee training program. After the program, 850 customers are tracked and it is found that only 7 of them
Deciphering Messages The Central Intelligence Agency has specialists who analyze the frequencies of letters of the alphabet in an attempt to decipher intercepted messages. In standard English text, the letter r is used at a rate of 7.7%.a. Find the mean and standard deviation for the number of
Analyzing Results of Experiment in Gender Selection An experiment involving a gender-selection method includes a control group of 15 couples who are not given any treatment intended to influence the genders of their babies. Each of the 15 couples has one child.a. Construct a table listing the
Left-Handed People Ten percent of American adults are left-handed. A statistics class has 25 students in attendance.a. Find the mean and standard deviation for the number of left-handed students in such classes of 25 students.b. Would it be unusual to survey a class of 25 students and find that 5
Playing Roulette If you bet on any single number in roulette, your probability of winning is 1 38. Assume that you bet on a single number in each of 100 consecutive spins.a. Find the mean and standard deviation for the number of wins.b. Would it be unusual to not win once in the 100 trials? Why or
Guessing Answers Several students are unprepared for a multiple-choice quiz with 10 questions, and all of their answers are guesses. Each question has five possible answers, and only one of them is correct.a. Find the mean and standard deviation for the number of correct answers for such
Taking Courses after Graduation The Market Research Institute found that among employed college graduates aged 30–55 and out of college for at least 10 years, 57%have taken college courses after graduation (as reported in USA Today). If you randomly select five college graduates aged 30–55 and
Testing Effectiveness of Gender-Selection Technique The Chapter Problem describes the probability distribution for the number of girls x when 14 newborn babies are randomly selected. Assume that another clinical experiment involves 12 newborn babies.Using the same format as Table 4-1, construct a
Author’s Slot Machine The author purchased a slot machine that is configured so that there is a 1 2000 probability of winning the jackpot on any individual trial. Although no one would seriously consider tricking the author, suppose that a guest claims that she played the slot machine five times
Identifying Gender Discrimination After being rejected for employment, Kim Kelly learns that the Bellevue Advertising Company has hired only two women among the last 20 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and
Affirmative Action Programs A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as affirmative action) and medical students admitted through the regular admissions criteria. It was found that the graduation
TV Viewer Surveys The CBS television show 60 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 60 Minutes (based on data from Nielsen Media Research). Assume that an advertiser wants to verify that 20% share
Drug Reaction In a clinical test of the drug Viagra, it was found that 4% of those in a placebo group experienced headaches.a. Assuming that the same 4% rate applies to those taking Viagra, find the probability that among eight Viagra users, three experience headaches.b. Assuming that the same 4%
(Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Find the probability that if Air America books 15 persons, not enough seats will be available. Is this probability low enough so that overbooking is not a real concern for passengers?
Overbooking Flights Air America has a policy of booking as many as 15 persons on an airplane that can seat only
Directory Assistance An article in USA Today stated that “Internal surveys paid for by directory assistance providers show that even the most accurate companies give out wrong numbers 15% of the time.” Assume that you are testing such a provider by making 10 requests and also assume that the
IRS Audits The Hemingway Financial Company prepares tax returns for individuals.(Motto: “We also write great fiction.”) According to the Internal Revenue Service, individuals making $25,000–$50,000 are audited at a rate of 1%. The Hemingway Company prepares five tax returns for individuals in
Acceptance Sampling The Telektronic Company purchases large shipments of fluorescent bulbs and uses this acceptance sampling plan: Randomly select and test 24 bulbs, then accept the whole batch if there is only one or none that doesn’t work. If a particular shipment of thousands of bulbs actually
Color Blindness Nine percent of men and 0.25% of women cannot distinguish between the colors red and green. This is the type of color blindness that causes problems with traffic signals. If six men are randomly selected for a study of traffic signal perceptions, find the probability that exactly
Find the probability that at least one American Airlines flight arrives on time. Is it unusual to not get at least one of six American Airlines flights arriving on time?
Find the probability that more than one American Airlines flight arrives on time. Is it unusual to not get more than one of six American Airlines flights arriving on time?
Find the probability that at most two American Airlines flights arrive on time. Is it unusual to have at most two of six American Airlines flights arriving on time?
Find the probability that at least five American Airlines flights arrive on time. Is it unusual to have at least five of six American Airlines flights arriving on time?
Labeling Dice to Get a Uniform Distribution Assume that you have two blank dice, so that you can label the 12 faces with any numbers. Describe how the dice can be labeled so that, when the two dice are rolled, the totals of the two dice are uniformly distributed so that the outcomes of 1, 2, 3, . .
Equally Likely Integers: Mean and Standard Deviation Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n, and those values are equally likely. This probability distribution has mean and standard deviation described as
Computer-Generated Numbers Transformed to z Scores Computers are often used to randomly generate the last digits of telephone numbers of potential survey subjects.The digits are selected so that they are all equally likely. The random variable x is the selected digit.a. Find the mean and standard
Defective Parts: Finding Mean and Standard Deviation The Sky Ranch is a supplier of aircraft parts. Included in stock are eight altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected without replacement. Let the random variable x represent the number
Finding Mean and Standard Deviation Let the random variable x represent the number of girls in a family of four children. Construct a table describing the probability distribution, then find the mean and standard deviation. (Hint: List the different possible outcomes.)
Junk Bonds Kim Hunter has $1000 to invest, and her financial analyst recommends two types of junk bonds. The A bonds have a 6% annual yield with a default rate of 1%. The B bonds have an 8% annual yield with a default rate of 5%. (If the bond defaults, the $1000 is lost.) Which of the two bonds is
Psychic Powers Bob is a self-proclaimed “mentalist” who claims that he can pass true false tests by guessing. In a test of Bob’s claim, he is given 14 true false questions, and Bob manages to correctly guess the answers to 2 of them. Is the number of correct answers unusual? Why or why not?
Psychic Powers Bob is a self-proclaimed “mentalist” who claims that he can pass true false tests by guessing. In a test of Bob’s claim, he is given 14 true false questions, and Bob manages to correctly guess the answers to 8 of them. He claims that getting 8 correct answers among 14 is proof
Determining Whether Gender-Selection Technique Is Effective Assume that in a test of a gender-selection technique, a clinical trial results in 10 girls in 14 births. Refer to Table 4-1 and find the indicated probability.a. What is the probability value that should be used for determining whether
Determining Whether Gender-Selection Technique Is Effective Assume that in a test of a gender-selection technique, a clinical trial results in 11 girls in 14 births. Refer to Table 4-1 and find the indicated probabilitya. What is the probability value that should be used for determining whether the
Determining Whether Gender-Selection Technique Is Effective Assume that in a test of a gender-selection technique, a clinical trial results in 12 girls in 14 births. Refer to Table 4-1 and find the indicated probabilities.a. Find the probability of exactly 12 girls in 14 births.b. Find the
Determining Whether Gender-Selection Technique Is Effective Assume that in a test of a gender-selection technique, a clinical trial results in 9 girls in 14 births. Refer to Table 4-1 and find the indicated probabilities.a. Find the probability of exactly 9 girls in 14 births.b. Find the
Finding Expected Value for the Illinois Pick 3 Game In Illinois’ Pick 3 game, you pay 50¢ to select a sequence of three digits, such as 911. If you win by selecting the same sequence of three digits that are drawn, you collect $250.a. How many different selections are possible?b. What is the
Finding Expected Value for New Jersey’s Pick 4 Game In New Jersey’s Pick 4 lottery game, you pay 50¢ to select a sequence of four digits, such as 7273. If you win by selecting the same sequence of four digits that are drawn, you collect $2788.a. How many different selections are possible?b.
Finding Expected Value for a Magazine Sweepstakes Reader’s Digest recently ran a sweepstakes in which prizes were listed along with the chances of winning:$1,000,000 (1 chance in 90,000,000), $100,000 (1 chance in 110,000,000), $25,000 (1 chance in 110,000,000), $5000 (1 chance in 36,667,000),
Finding Expected Value for a Life Insurance Policy The CNA Insurance Company charges Mike $250 for a one-year $100,000 life insurance policy. Because Mike is a 21-year-old male, there is a 0.9985 probability that he will live for a year (based on data from U.S. National Center for Health
Finding Expected Value in Roulette When you give a casino $5 for a bet on the number 7 in roulette, you have a 1 38 probability of winning $175 and a 37 38 probability of losing $5. If you bet $5 that the outcome is an odd number, the probability of winning $5 is 18 38, and the probability of
Finding Expected Value in Craps When you give a casino $5 for a bet on the “pass line” in the game of craps, there is a 244 495 probability that you will win $5 and a 251 495 probability that you will lose $5. What is your expected value? In the long run, how much do you lose for each dollar
Brand Recognition In a study of brand recognition of Sony, groups of four consumers are interviewed. If x is the number of people in the group who recognize the Sony brand name, then x can be 0, 1, 2, 3, or 4, and the corresponding probabilities are 0.0016, 0.0250, 0.1432, 0.3892, and 0.4096. Is it
Number of Games in a Baseball World Series Based on past results found in the Information Please Almanac, there is a 0.1809 probability that a baseball World Series contest will last four games, a 0.2234 probability that it will last five games, a 0.2234 probability that it will last six games, and
Life Insurance The New England Life Insurance Company issues one-year policies to 12 men who are all 27 years of age. Based on data from the Department of Health and Human Services, each of these men has a 99.82% chance of living through the year. What is the probability that they all survive the
Is the Pollster Lying? A pollster claims that 12 voters were randomly selected from a population of 200,000 voters (30% of whom are Republicans), and all 12 were Republicans. The pollster claims that this could easily happen by chance. Find the probability of getting 12 Republicans when 12 voters
Roulette When betting on even in roulette, there are 38 equally likely outcomes, but only 2, 4, 6, . . . , 36 are winning outcomes.a. Find the probability of winning when betting on even.b. Find the actual odds against winning with a bet on even.c. Casinos pay winning bets according to odds
Selecting Members The board of directors for the Hartford Investment Fund has 10 members.a. If 3 members are randomly selected to oversee the auditors, find the probability that the three wealthiest members are selected.b. If members are elected to the positions of chairperson, vice chairperson,
Testing a Claim The Biogene Research Company claims that it has developed a technique for ensuring that a baby will be a girl. In a test of that technique, 12 couples all have baby girls. Find the probability of getting 12 baby girls by chance, assuming that boys and girls are equally likely and
Acceptance Sampling With one method of acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is rejected if there is at least one defect. The Niko Electronics Company has just manufactured 2500 CDs, and 2% are defective. If 4 of the CDs are selected
Probability of Computer Failures A PC World survey of 4000 personal computer owners showed that 992 of them broke down during the first two years. (The computers broke down, not the owners.) In choosing among several computer suppliers, a purchasing agent wants to know the probability of a personal
Computer Intelligence Can computers “think”? According to the Turing test, a computer can be considered to think if, when a person communicates with it, the person believes he or she is communicating with another person instead of a computer. In an experiment at Boston’s Computer Museum, each
Evaluating Large Factorials Many calculators or computers cannot directly calculate 70! or higher. When n is large, n! can be approximated by n 5 10K, where K 5(n 1 0.5) log n 1 0.39908993 2 0.43429448n.a. Evaluate 50! using the factorial key on a calculator and also by using the approximation
Handshakes and Round Tablesa. Five managers gather for a meeting. If each manager shakes hands with each other manager exactly once, what is the total number of handshakes?b. If n managers shake hands with each other exactly once, what is the total number of handshakes?c. How many different ways
Finding the Number of Computer Variable Names A common computer programming rule is that names of variables must be between 1 and 8 characters long. The first character can be any of the 26 letters, while successive characters can be any of the 26 letters or any of the 10 digits. For example,
N.C.A.A. Basketball Tournament Each year, 64 college basketball teams compete in the N.C.A.A. tournament. Sandbox.com recently offered a prize of $10 million to anyone who could correctly pick the winner in each of the tournament games. The president of that company also promised that, in addition
California Lottery In California’s Super Lotto Plus lottery game, winning the jackpot requires that you select the correct 5 numbers between 1 and 47 and, in a separate drawing, you must also select the correct single number between 1 and 27. Find the probability of winning the jackpot.
Cracked Eggs A carton contains 12 eggs, 3 of which are cracked. If we randomly select 5 of the eggs for hard boiling, what is the probability of the following events?a. All of the cracked eggs are selected.b. None of the cracked eggs are selected.c. Two of the cracked eggs are selected.
Finding the Number of Area Codes USA Today reporter Paul Wiseman described the old rules for telephone area codes by writing about “possible area codes with 1 or 0 in the second digit. (Excluded: codes ending in 00 or 11, for toll-free calls, emergency services, and other special uses.)” Codes
Is the Researcher Cheating? You become suspicious when a genetics researcher randomly selects groups of 20 newborn babies and seems to consistently get 10 girls and 10 boys. The researcher explains that it is common to get 10 boys and 10 girls in such cases.a. If 20 newborn babies are randomly
Probabilities of Gender Sequencesa. If a couple plans to have eight children, how many different gender sequences are possible?b. If a couple has four boys and four girls, how many different gender sequences are possible?c. Based on the results from parts (a) and (b), what is the probability that
Five Card Flush A standard deck of cards contains 13 clubs, 13 diamonds, 13 hearts, and 13 spades. If five cards are randomly selected, find the probability of getting a flush. (A flush is obtained when all five cards are of the same suit. That is, they are all clubs, or all diamonds, or all
Combination Locks A typical “combination” lock is opened with the correct sequence of three numbers between 0 and 49 inclusive. (A number can be used more than once.) What is the probability of guessing those three numbers and opening the lock with the first try?
Finding the Number of Possible Melodies In Denys Parsons’ Directory of Tunes and Musical Themes, melodies for more than 14,000 songs are listed according to the following scheme: The first note of every song is represented by an asterisk *, and successive notes are represented by R (for repeat
Jumble Puzzle Many newspapers carry “Jumble,” a puzzle in which the reader must unscramble letters to form words. For example, the letters TAISER were included in newspapers on the day this exercise was written. How many ways can the letters of TAISER be arranged? Identify the correct
Elected Board of Directors There are 12 members on the board of directors for the Newport General Hospital.a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible?b. If they must form an ethics
Electrifying When testing for electrical current in a cable with five color-coded wires, the author used a meter to test two wires at a time. How many tests are required for every possible pairing of two wires?
Social Security Numbers Each social security number is a sequence of nine digits.What is the probability of randomly generating nine digits and getting your social security number?
Air Routes You have just started your own airline company called Air America(motto: “Where your probability of a safe flight is greater than zero”). You have one plane for a route connecting Austin, Boise, and Chicago. One route is Austin-BoiseChicago and a second route is Chicago-Boise-Austin.
He Did It His Way Singing legend Frank Sinatra recorded 381 songs. From a list of his top-10 songs, you must select three that will be sung in a medley as a tribute at the next MTV Music Awards ceremony. The order of the songs is important so that they fit together well. If you select three of
Selection of Treatment Group Walton Pharmaceuticals wants to test the effectiveness of a new drug designed to relieve allergy symptoms. The initial test will be conducted by treating six people chosen from a pool of 15 volunteers. If the treatment group is randomly selected, what is the probability
Testing a Claim Mike claims that he has developed the ability to roll a 6 almost every time that he rolls a die. You test his claim by having Mike roll a die five times, and he gets a 6 each time. If Mike has no ability to affect the outcomes, find the probability that he will roll five consecutive
Maine Lottery The probability of winning the Maine lottery is 1 5,245,786. What is the probability of winning if the rules are changed so that in addition to selecting the correct six numbers from 1 to 42, you must now select them in the same order as they are drawn?
Computer Design In designing a computer, if a byte is defined to be a sequence of 8 bits and each bit must be a 0 or 1, how many different bytes are possible? (A byte is often used to represent an individual character, such as a letter, digit, or punctuation symbol. For example, one coding system
Age Discrimination The Pitt Software Company reduced its sales staff from 32 employees to 28. The company claimed that four employees were randomly selected for job termination. However, the four employees chosen are the four oldest employees among the original sales force of 32. Find the
Unseen Coins A statistics professor tosses two coins that cannot be seen by any students. One student asks if one of the coins turned up heads. Given that the professor’s response is “yes,” find the probability that both coins turned up heads.
Shared Birthdays Find the probability that of 25 randomly selected people,a. no two share the same birthday.b. at least two share the same birthday.
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