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Elementary Statistics 10th Edition Mario F. Triola - Solutions
27. 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
26. 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
25. Frequency Distribution and Probability Distribution What is the fundamental difference between a frequency distribution (as defined in Section 2-2) and a probability distribution (as defined in this section)?
24. Home Sales Refer to the numbers of bedrooms in homes sold, as listed in Data Set 18 in Appendix B. Use the frequency distribution to construct a table representing the probability distribution, then find the mean and standard deviation. Also, describe the shape of the probability histogram.5-2
23. Telephone Surveys Computers are often used to randomly generate digits of telephone numbers to be called for surveys. Each digit has the same chance of being>>>>>>5-3 Binomial Probability Distributions 213 selected. Construct a table representing the probability distribution for the digits
22. 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.) Is it unusual for a
21. Finding Mean and Standard Deviation Let the random variable x represent the number of girls in a family of three children. Construct a table describing the probability distribution, then find the mean and standard deviation. (Hint: List the different possible outcomes.) Is it unusual for a
20. Expected Value for a Magazine Sweepstakes Reader’s Digest 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),$5,000 (1 chance in 36,667,000), and $2,500 (1
19. Expected Value for a Life Insurance Policy The CNA Insurance Company charges a 21-year-old male a premium of $250 for a one-year $100,000 life insurance policy. A 21-year-old male has a 0.9985 probability of living for a year (based on data from the National Center for Health Statistics).a.
18. Expected Value in Casino Dice When you give a casino $5 for a bet on the “pass line” in a casino game of dice, there is a 251 495 probability that you will lose $5 and there is a 244 495 probability that you will make a net gain of $5. (If you win, the casino gives you $5 and you get to
17. Expected Value in Roulette When you give the Venetian casino in Las Vegas $5 for a bet on the number 7 in roulette, you have a 37 38 probability of losing $5 and you have a 1 38 probability of making a net gain of $175. (The prize is $180, including your $5 bet, so the net gain is $175.) If you
16. Determining Whether a Jury Selection Process Is Biased Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probability.a. Using the probability values in Table 5-1, find the probability value
15. Determining Whether a Jury Selection Process Discriminates Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probability.a. Using the probability values in Table 5-1, find the probability
14. Determining Whether a Jury Selection Process Discriminates Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probabilities.a. Find the probability of exactly 6 Mexican-Americans among 12
13. Determining Whether a Jury Selection Process Discriminates Assume that 12 jurors are randomly selected from a population in which 80% of the people are Mexican-Americans. Refer to Table 5-1 and find the indicated probabilities.a. Find the probability of exactly 5 Mexican-Americans among 12
12. 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.
11. Number of Games in a Baseball World Series Based on past results found in the Information Please Almanac, there is a 0.1818 probability that a baseball World Series contest will last four games, a 0.2121 probability that it will last five games, a 0.2323 probability that it will last six games,
10. Mortality Study For a group of four men, the probability distribution for the number x who live through the next year is as given in the accompanying table.
9. Genetics Experiment A genetics experiment involves offspring peas in groups of four. A researcher reports that for one group, the number of peas with white flowers has a probability distribution as given in the accompanying table.x P(x)0 0.4219 1 0.4219 2 0.1406 3 0.0156 x P(x)0 0.502 1 0.365 2
8. Numbers of Girls A researcher reports that when groups of four children are randomly selected from a population of couples meeting certain criteria, the probability distribution for the number of girls is as given in the accompanying table.
7. Genetic Disorder Three males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the three who inherit the X-linked genetic disorder.
6.a. The cost of conducting a genetics experimentb. The number of supermodels who ate pizza yesterdayc. The exact life span of a kittend. The number of statistics professors who read a newspaper each daye. The weight of a feather Identifying Probability Distributions. In Exercises 7–12, determine
5.a. The height of a randomly selected giraffe living in Kenyab. The number of bald eagles located in New York Statec. The exact time it takes to evaluate 27 72.d. The number of textbook authors now sitting at a computere. The number of statistics students now reading a book
4. Expected Value A researcher calculates the expected value for the number of girls in five births. He gets a result of 2.5. He then rounds the result to 3, saying that it is not possible to get 2.5 girls when five babies are born. Is this reasoning correct?Identifying Discrete and Continuous
3. Probability Distribution A professional gambler claims that he has loaded a die so that the outcomes of 1, 2, 3, 4, 5, 6 have corresponding probabilities of 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6. Can he actually do what he has claimed? Is a probability distribution described by listing the outcomes
2. Probability Distribution One of the requirements of a probability distribution is that the sum of the probabilities must be 1 (with a small amount of leeway allowed for rounding errors). What is the justification for this requirement?
10. Do you think that this estimate is somewhat accurate?Why or why not?d. Using the results from part (b), estimate the probability that the number of defects in a batch is exactly 9.e. After examining the results from part (b), how much do the numbers of defects vary? Are the numbers of defects
In Exercise 11 from Section 4-6, we referred to a process of manufacturing cell phones. We assumed that a batch consists of 500 cell phones and the overall rate of defective cell phones is 2%. We can conduct a simulation by generating 500 numbers, with each number between 1 and 100 inclusive.
5. Out-of-class activity Divide into groups of two for the purpose of doing an experiment designed to show one approach to dealing with sensitive survey questions, such as those related to drug use, sexual activity (or inactivity), stealing, or cheating. Instead of actually using a controversial
4. In-class activity Divide into groups of two. Refer to Exercise 15 in Section 4-6 for a description of the“Monty Hall problem.” Simulate the contest and record the results for sticking and switching, then determine which of those two strategies is better.
3. Out-of-class activity Marine biologists often use the capture-recapture method as a way to estimate the size of a population, such as the number of fish in a lake.This method involves capturing a sample from the population, tagging each member in the sample, then returning them to the
2. In-class activity Divide into groups of three or four and use actual thumbtacks to estimate the probability that when dropped, a thumbtack will land with the point up.How many trials are necessary to get a result that appears to be reasonably accurate when rounded to the first decimal place?
1. In-class activity Divide into groups of three or four and use coin tossing to develop a simulation that emulates the kingdom that abides by this decree: After a mother gives birth to a son, she will not have any other children.If this decree is followed, does the proportion of girls increase?
16. Bar Codes On January 1, 2005, the bar codes put on retail products were changed so that they now represent 13 digits instead of 12. How many different products can now be identified with the new bar codes?
15. Chlamydia Rate For a recent year, the rate of chlamydia was reported as 278.32 per 100,000 population.a. Find the probability that a randomly selected person has chlamydia.b. If two people are randomly selected, find the probability that they both have chlamydia, and express the result using
14. 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 Medtyme Pharmaceutical Company has just manufactured 2500 aspirin tablets, and 2% are defective because
13. 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. What is the probability that the two live wires are located with the first random selection of two wires?
12. 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
11. 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
10. Fruitcake Survey In a Bruskin-Goldring Research poll, respondents were asked how a fruitcake should be used. The respondents consist of 132 people indicating that it should be used for a doorstop, and 880 other people who gave other uses, including birdfeed, landfill, and a gift. If one of
41. Change for a Dollar How many different ways can you make change for a dollar?9. National Statistics Daya. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years.b. If a person is randomly
40. 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,
39. 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. You have been hired to visit the capitol of each of the 50 states. How many different
38. 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
37. 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,
36. Power Ball Lottery The Power Ball lottery is run in 27 states. Winning a Power Ball lottery jackpot requires that you select the correct five numbers between 1 and 53 inclusive and, in a separate drawing, you must also select the correct single number between 1 and 42 inclusive. Find the
35. California Lottery In California’s Super Lotto Plus lottery game, winning the jackpot requires that you select the correct five numbers between 1 and 47 inclusive and, in a separate drawing, you must also select the correct single number between 1 and 27 inclusive.Find the probability of
34. ATM Machine You want to obtain cash by using an ATM machine, but it’s dark and you can’t see your card when you insert it. The card must be inserted with the front side up and the printing configured so that the beginning of your name enters first.a. What is the probability of selecting a
33. NCAABasketball Tournament Each year, 64 college basketball teams compete in the NCAA 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 to
32. 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.
31. Finding the Number of Area Codes USA Today reporter Paul Wiseman described the old rules for the three-digit 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
30. 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?
29. 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
28. 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
27. 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
26. Gender Selection In a test of a gender-selection method, 14 babies are born and 10 of them are girls.a. Find the number of different possible sequences of genders that are possible when 14 babies are born.b. How many ways can 10 girls and 4 boys be arranged in a sequence?c. If 14 babies are
25. 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
24. Air Routes You have just started your own airline company named Air Me (motto:“To us, you are not just another statistic”). So far, you have one plane for a route connecting Austin, Boise, and Chicago. One route is Austin–Boise–Chicago and a second route is Chicago–Boise–Austin. How
23. Probability of Defective Pills A batch of pills consists of 7 that are good and 3 that are defective (because they contain the wrong amount of the drug).a. How many different permutations are possible when all 10 pills are randomly selected(without replacement)?b. If 3 pills are randomly
22. Design of Experiments In designing an experiment involving a treatment applied to 12 test subjects, researchers plan to use a simple random sample of 12 subjects selected from a pool of 20 available subjects. (Recall that with a simple random sample, all samples of the same size have the same
21. Tree Growth Experiment When designing an experiment to study tree growth, the following four treatments are used: none, irrigation only, fertilization only, irrigation and fertilization. A row of 10 trees extends from a moist creek bed to a dry land area.If one of the four treatments is
20. 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
19. Age Discrimination The Cytertonics Communications Company reduced its management staff from 15 managers to 10. The company claimed that five managers were randomly selected for job termination. However, the five managers chosen are the five oldest managers among the 15 that were employed. Find
18. DNANucleotides DNA(deoxyribonucleic acid) is made of nucleotides, and each nucleotide can contain any one of these nitrogenous bases: A (adenine), G (guanine), C(cytosine), T (thymine). If one of those four bases (A, G, C, T) must be selected three times to form a linear triplet, how many
4. Probability Someone reasons that when a coin is tossed, there are three possible outcomes: It comes up heads or tails or it lands on its edge. With three outcomes on each toss, the fundamental counting rule suggests that there are nine possibilities(from ) for two tosses of a coin. It therefore
3. Relative Frequency A researcher is analyzing a large sample of text in order to find the relative frequency of the word “zip” among three-letter words. That is, she wants to estimate the probability of getting the word “zip” when a three-letter word is randomly selected from typical
2. Counting When trying to find the probability of winning the California Fantasy 5 lottery, it becomes necessary to find the number of different outcomes that can occur when 5 numbers between 1 and 39 are selected. Why can’t that number be found by simply listing all of the possibilities?
1. Permutations and Combinations What is the basic difference between a situation requiring application of the permutations rule and one that requires the combinations rule?
17. Genetics: Simulating Population Control A classical probability problem involves a king who wanted to increase the proportion of women by decreeing that after a mother gives birth to a son, she is prohibited from having any more children. The king reasons that some families will have just one
16. Simulating Birthdaysa. Develop a simulation for finding the probability that when 50 people are randomly selected, at least 2 of them have the same birth date. Describe the simulation and estimate the probability.b. Develop a simulation for finding the probability that when 50 people are
15. Simulating the Monty Hall Problem A problem that has attracted much attention in recent years is the Monty Hall problem, based on the old television game show “Let’s Make a Deal,” hosted by Monty Hall. Suppose you are a contestant who has selected one of three doors after being told that
14. Analyzing the Effectiveness of a Gender-Selection Method When testing the effectiveness of a gender-selection technique, a trial was conducted with 20 couples trying to have a baby girl. Among the 20 babies that were born, there were 18 girls. Conduct a simulation of 20 births assuming that the
13. Analyzing the Effectiveness of a Drug It has been found that when someone tries to stop smoking under certain circumstances, the success rate is 20%. A new nicotine substitute drug has been designed to help those who wish to stop smoking. In a trial of>>>178 Chapter 4 Probability 50 smokers who
12. Simulating Left-Handedness Refer to Exercise 8, which required a description of a simulation.a. Conduct the simulation and record the number of left-handed men. Is the percentage of left-handed men from the simulation reasonably close to the value of 15%?b. Repeat the simulation until it has
11. Simulating Manufacturing Refer to Exercise 7, which required a description of a manufacturing simulation.a. Conduct the simulation and record the number of defective cell phones. Is the percentage of defective cell phones from the simulation reasonably close to the value of 2%?b. Repeat the
10. Simulating Hybridization Refer to Exercise 6, which required a description of a hybridization simulation.a. Conduct the simulation and record the number of yellow peas. If possible, obtain a printed copy of the results. Is the percentage of yellow peas from the simulation reasonably close to
9. Simulating Motorcycle Safety Study Refer to Exercise 5, which required a description of a simulation.a. Conduct the simulation and record the number of male motorcycle drivers. If possible, obtain a printed copy of the results. Is the percentage of males from the simulation reasonably close to
8. Simulating Left-Handedness Fifteen percent of U.S. men are left-handed (based on data from a Scripps Survey Research Center poll). Describe a procedure for using software or a TI-83 84 Plus calculator to simulate the random selection of 200 men. The outcomes should consist of an indication of
7. Simulating Manufacturing Describe a procedure for using software or a TI-83 84 Plus calculator to simulate 500 manufactured cell phones. For each cell phone, the result should consist of an indication of whether the cell phone is good or defective. The manufacturing process has a defect rate of
6. Simulating Hybridization When Mendel conducted his famous hybridization experiments, he used peas with green pods and yellow pods. One experiment involved crossing peas in such a way that 25% of the offspring peas were expected to have yellow pods, and 75% of the offspring peas were expected to
5. Simulating Motorcycle Safety Study In a study of fatalities caused by motorcycle crashes, it was found that 95% of motorcycle drivers are men (based on data from“Motorcycle Rider Conspicuity and Crash Related Injury,” by Wells et al., BJM USA).Describe a procedure for using software or a
4. Simulation A student wants to simulate three births, so she writes “male” on one index card and “female” on another. She shuffles the cards, then selects one and records the gender. She shuffles the cards a second time, selects one and records the gender.She shuffles the cards a third
3. Simulation A student wants to simulate 25 birthdays as described in this section, but she does not have a calculator or software program available, so she makes up 25 numbers between 1 and 365. Is it okay to conduct the simulation this way? Why or why not?
2. Simulation When three babies are born, there can be 0 girls, 1 girl, 2 girls, or 3 girls.A researcher simulates three births as follows: The number 0 is written on one index card, the number 1 is written on another index card, 2 is written on a third card, and 3 is written on a fourth card. The
1. Simulations What is a simulation? If a simulation method is used for a probability problem, is the result the exact correct answer?
24. If we randomly select one Senator, what is the probability of getting a Democrat or Independent, given that a male was selected?
23. If we randomly select one Senator, what is the probability of getting a female, given that an Independent was selected?
22. If we randomly select one Senator, what is the probability of getting a male, given that a Republican was selected? Is this the same result found in Exercise 21?
21. If we randomly select one Senator, what is the probability of getting a Republican, given that a male was selected?
20. Using Composite Water Samples The Orange County Department of Public Health tests water for contamination due to the presence of E. coli (Escherichia coli) bacteria.To reduce laboratory costs, water samples from six public swimming areas are combined for one test, and further testing is done
19. Using Composite Blood Samples When doing blood testing for HIV infections, the procedure can be made more efficient and less expensive by combining samples of blood specimens. If samples from three people are combined and the mixture tests negative, we know that all three individual samples are
18. Acceptance Sampling With one method of the procedure called 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 Medtyme Company has just manufactured 5000 blood pressure monitors, and 4% are
17. Redundancy in Alarm Clocks A statistics professor wants to ensure that she is not late for an early class because of a malfunctioning alarm clock. Instead of using one alarm clock, she decides to use three. What is the probability that at least one of her alarm clocks works correctly if each
16. Drug Testing Refer to Table 4-1 and assume that 1 of the 300 test subjects is randomly selected. Find the probability of getting someone who did not use marijuana, given that he or she tested negative. Compare this result and the result found in Exercise 15.>172 Chapter 4 Probability
15. Drug Testing Refer to Table 4-1 and assume that 1 of the 300 test subjects is randomly selected. Find the probability of getting someone who tests negative, given that he or she did not use marijuana.
14. Drug Testing Refer to Table 4-1 and assume that 1 of the 300 test subjects is randomly selected. Find the probability of getting someone who tests positive, given that he or she did not use marijuana. Why is this particular case problematic for test subjects?
13. Probability of a Girl Find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. Is the result the same as the probability of getting three girls among three children?
12. Probability of At Least One Girl If a couple plans to have 10 children (it could happen), what is the probability that there will be at least one girl? If the couple eventually has 10 children and they are all boys, what can the couple conclude?
11. Probability of At Least One Girl If a couple plans to have four children, what is the probability that they will have at least one girl? Is that probability high enough for the couple to be very confident that they will get at least one girl in four children?
10. Subjective Conditional Probability Use subjective probability to estimate the probability of randomly selecting an adult and getting a male, given that the selected person owns a motorcycle. If a criminal investigator finds that a motorcycle is registered to Pat Ryan, is it reasonable to
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