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Elementary Statistics 10th Edition Mario F. Triola - Solutions
5. Blood Testing When six job applicants are tested for use of marijuana, at least one of them tests positive.6. Quality Control When 50 electrocardiograph units are shipped, all of them are free of defects.7. X-Linked Disorder When 12 males are tested for a particular X-linked recessive gene, none
4. Confusion of the Inverse What is confusion of the inverse?Describing Complements. In Exercises 5–8, provide a written description of the complement of the given event.
3. Finding Probability A market researcher needs to find the probability that a shopper is male, given that a credit card was used for a purchase. He reasons that there are two outcomes (male, female), so the probability is 1 2. Is he correct? What important information is not included in his
2. Conditional Probability In your own words, describe conditional probability and give an example.
23. Drawing Cards Two cards are to be randomly selected without replacement from a shuffled deck. Find the probability of getting an ace on the first card and a spade on the second card.1. Probability of at Least One You want to find the probability of getting at least 1 defect when 10 heart
22. Gender of Childrena. If a couple plans to have eight children, find the probability that they are all of the same gender.b. Assuming that boys and girls are equally likely, find the probability of getting all girls when 1000 babies are born. Does the result indicate that such an event is
21. Same Birthdays Find the probability that no two people have the same birthday when the number of randomly selected people isa. 3b. 5c. 25
20. Pedestrian Deathsa. If one of the pedestrian deaths is randomly selected, what is the probability that it involves an intoxicated pedestrian and an intoxicated driver?b. If two different pedestrian deaths are randomly selected, what is the probability that in both cases, both the pedestrian and
19. Pedestrian Deathsa. If one of the pedestrian deaths is randomly selected, what is the probability that it involves a case in which neither the pedestrian nor the driver was intoxicated?b. If two different pedestrian deaths are randomly selected, what is the probability that in both cases,
18. Intoxicated Pedestrians If two different pedestrian deaths are randomly selected, find the probability that they both involve intoxicated pedestrians.
17. Intoxicated Drivers If two different pedestrian deaths are randomly selected, find the probability that they both involved intoxicated drivers.
16. Social Skills Bob reasons that when he asks a woman for a date, she can accept or reject his request, so he assumes that he has a 0.5 probability of getting a date. If his assumption is correct, what is the probability of getting five rejections when Bob asks five different women for dates? Is
15. Redundancy The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that your alarm clock has a 0.975 probability of working on any given morning.a. What is the probability that your alarm clock will not work on the morning of an
14. Voice Identification of Criminal In a Riverhead, New York, case, nine different crime victims listened to voice recordings of five different men. All nine victims identified the same voice as that of the criminal. If the voice identifications were made by random guesses, find the probability
13. Testing Effectiveness of Gender-Selection Method Recent developments appear to make it possible for couples to dramatically increase the likelihood that they will conceive a child with the gender of their choice. In a test of a gender-selection method, 12 couples try to have baby girls. If this
12. Poll Confidence Level It is common for public opinion polls to have a “confidence level” of 95%, meaning that there is a 0.95 probability that the poll results are accurate within the claimed margins of error. If six different organizations conduct independent polls, what is the probability
11. Acceptance Sampling With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The Niko Electronics Company has just manufactured 5000 CDs, and 100 are defective. If
10. Selecting U.S. Senators In the 108th Congress, the Senate consists of 51 Republicans, 48 Democrats, and 1 Independent. If a lobbyist for the tobacco industry randomly selects three different Senators, what is the probability that they are all Republicans?Would a lobbyist be likely to use random
9. Wearing Hunter Orange A study of hunting injuries and the wearing of “hunter”orange clothing showed that among 123 hunters injured when mistaken for game, 6 were wearing orange (based on data from the Centers for Disease Control). If a follow-up study begins with the random selection of
8. Letter and Digit A new computer owner creates a password consisting of two characters.She randomly selects a letter of the alphabet for the first character and a digit(0, 1, 2, 3, 4, 5, 6, 7, 8, 9) for the second character. What is the probability that her password is “K9”? Would this
7. Guessing A quick quiz consists of a true false question followed by a multiplechoice question with four possible answers (a,b, c, d). If both questions are answered with random guesses, find the probability that both responses are correct. Does guessing appear to be a good strategy on this quiz?
6.a. Finding that your calculator is working Finding that your cell phone is workingb. Finding that your kitchen toaster is not working Finding that your refrigerator is not workingc. Drinking or using drugs until your driving ability is impaired Being involved in a car crash
5.a. Randomly selecting a quarter made before 2001 Randomly selecting a second quarter made before 2001b. Randomly selecting a TV viewer who is watching The Barry Manilow Biography Randomly selecting a second TV viewer who is watching The Barry Manilow Biographyc. Wearing plaid shorts with black
4. Notation What does the notation represent?Identifying Events as Independent or Dependent. In Exercises 5 and 6, for each given pair of events, classify the two events as independent or dependent. (If two events are technically dependent but can be treated as if they are independent, consider
3. Sampling Without Replacement The professor in a class of 25 students randomly selects a student, then randomly selects a second student. If 24 students are available for the second selection, is this sampling with replacement or sampling without replacement?Is the second outcome independent of
2. Sampling With Replacement The professor in a class of 25 students randomly selects a student, then randomly selects a second student. If all 25 students are available for the second selection, is this sampling with replacement or sampling without replacement?Is the second outcome independent of
1. Independent Events In your own words, state what it means for two events to be independent.
22. Hybridization Experiment Assume that one of the peas is randomly selected.a. Refer to the figure and find P(green pod or purple flower).b. Refer to the table completed in Exercise 21 and find P(green pod or purple flower).c. Which format is easier to use: the figure or the table?
21. Constructing Table Use the figure to identify the frequencies in the accompanying table. (The flowers are the top portions of the peas, and the pods are the bottom portions.)
20. Blood Groups and Types If one person is randomly selected, find P(group A or O or type Rh1).In Exercises 21 and 22, refer to the figure (on the top of the next page) depicting peas used in a genetics study. (Probabilities play a prominent role in genetics, and Mendel conducted famous
19. Blood Groups and Types If one person is randomly selected, find P(group AB or type Rh1).
18. Blood Groups and Types If one person is randomly selected, find P(group B or type Rh1).
17. Blood Groups and Types If one person is randomly selected, find P(not type Rh1).
16. Blood Groups and Types If one person is randomly selected, find the probability of getting someone who is group A or group B.
15. Blood Groups and Types If one person is randomly selected, find the probability of getting someone who is group A or type Rh2.
14. Blood Groups and Types If one person is randomly selected, find the probability of getting someone who is type Rh2.
13. Blood Groups and Types If one person is randomly selected, find the probability of getting someone who is not group A.
12. Pedestrian Deaths If one of the pedestrian deaths is randomly selected, find the probability that the driver was intoxicated or the pedestrian was not intoxicated.In Exercises 13–20, use the data in the following table, which summarizes blood groups and Rh types for 100 typical people. These
11. Pedestrian Deaths If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was not intoxicated.
10. Pedestrian Deaths If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
9. Pedestrian Deaths If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was intoxicated or the driver was intoxicated.
8. Finding Complementsa. Find given that P(A) 5 0.01.b. A Reuters Zogby poll showed that 61% of Americans say they believe that life exists elsewhere in the galaxy. What is the probability of randomly selecting someone not having that belief?In Exercises 9–12, use the data in the following table,
7. Finding Complementsa. If P(A) 5 0.05, findb. Women have a 0.25% rate of red green color blindness. If a woman is randomly selected, what is the probability that she does not have red green color blindness?(Hint: The decimal equivalent of 0.25% is 0.0025, not 0.25.)
6.a. Randomly selecting a fruit fly with red eyes Randomly selecting a fruit fly with sepian (dark brown) eyesb. Receiving a phone call from a volunteer survey subject who opposes all cloning Receiving a phone call from a volunteer survey subject who approves of cloning of sheepc. Randomly
5.a. Electing a president of the United States Electing a female candidateb. Randomly selecting someone who smokes cigars Randomly selecting a malec. Randomly selecting someone treated with the cholesterol-reducing drug Lipitor Randomly selecting someone in a control group given no medication
4. Disjoint Events and Complements If an event is the complement of another event, must those two events be disjoint? Why or why not?Determining Whether Events Are Disjoint. For each part of Exercises 5 and 6, are the two events disjoint for a single trial? (Hint: Consider “disjoint” to be
3. Survey For a research project, you need to find the probability that someone is lefthanded or drives a car. What is wrong with surveying 500 of your closest friends and relatives?
2. Addition Rule In your own words, describe how the addition rule is applied to finding the probability that event A occurs or event B occurs.
1. Disjoint Events In your own words, describe what it means for two events to be disjoint.
32. Kentucky Derby Odds When the horse Funny Cide won the 129th Kentucky Derby, a$2 bet that Funny Cide would win resulted in a return of $27.60.a. How much net profit was made from a $2 win bet on Funny Cide?b. What were the payoff odds against a Funny Cide win?c. Based on preliminary wagering
31. Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You are placing a bet that the outcome is an odd number.a. What is your probability of winning?b. What are the actual odds against winning?c. When you
30. Kentucky Derby Odds The probability of the horse Outta Here winning the 129th Kentucky Derby was What were the actual odds against Outta Here winning that race?
29. Solitaire Odds Because the calculations involved with solitaire are so complex, the game was played 500 times so that the probability of winning could be estimated.(The results are from the Microsoft solitaire game, and the Vegas rules of “draw 3”with $52 bet and a return of $5 per card are
28. Genetics: Constructing Sample Space Repeat Exercise 26 assuming that one parent has a brown brown pair of eye color genes while the other parent has a blue blue pair of eye color genes.Odds. In Exercises 29–32, answer the given questions that involve odds.
27. Genetics: Constructing Sample Space Repeat Exercise 26 assuming that one parent has a brown brown pair of eye color genes while the other parent has a brown blue pair of eye color genes.> >>>4-2 Fundamentals 149
26. Genetics: Constructing Sample Space Both parents have the brown blue pair of eye color genes, and each parent contributes one gene to a child. Assume that if the child has at least one brown gene, that color will dominate and the eyes will be brown. (The actual determination of eye color is
25. Gender of Children: Constructing Sample Space This section included a table summarizing the gender outcomes for a couple planning to have three children.a. Construct a similar table for a couple planning to have two children.b. Assuming that the outcomes listed in part (a) are equally likely,
24. Probability of a Wrong Result Table 4-1 shows that among 122 subjects who did use marijuana, the test result for marijuana usage was wrong 3 times.a. Based on the available results, find the probability of a wrong test result for a person who does use marijuana.b. Is it “unusual” for the
23. Probability of a Wrong Result Table 4-1 shows that among 178 subjects who did not use marijuana, the test result for marijuana usage was wrong 24 times.a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana.b. Is it “unusual”
22. Interpreting Effectiveness of a Treatment A double-blind experiment is designed to test the effectiveness of the drug Statisticzene as a treatment for number blindness.When treated with Statisticzene, subjects seem to show improvement. Researchers calculate that there is a 0.04 probability that
21. Adverse Effect of Viagra When the drug Viagra was clinically tested, 117 patients reported headaches and 617 did not (based on data from Pfizer, Inc.). Use this sample to estimate the probability that a Viagra user will experience a headache. Is it unusual for a Viagra user to experience
20. Adverse Effect of Lipitor In a clinical trial of Lipitor (atorvastatin), a common drug used to lower cholesterol, one group of patients was given a treatment of 10-mg atorvastatin tablets. That group consists of 19 patients who experienced flu symptoms and 844 patients who did not (based on
19. Probability of a Car Crash Among 400 randomly selected drivers in the 20–24 age bracket, 136 were in a car crash during the last year (based on data from the National Safety Council). If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will
18. IRS Accuracy The U.S. General Accounting Office tested the Internal Revenue Service for correctness of answers to taxpayers’ questions. For 1733 trials, the IRS was correct 1107 times and wrong 626 times.a. Estimate the probability that a randomly selected taxpayer’s question will be
17. Guessing Birthdays On their first date, Kelly asks Mike to guess the date of her birth, not including the year.a. What is the probability that Mike will guess correctly? (Ignore leap years.)b. Would it be unusual for him to guess correctly on his first try?c. If you were Kelly, and Mike did
16. Pedestrian Walk Buttons New York City has 750 pedestrian walk buttons that work, and another 2500 that do not work (based on data from “For Exercise in New York Futility, Push Button,” by Michael Luo, New York Times). If a pedestrian walk button is randomly selected in New York City, what
15. Blue M&M Plain Candiesa. Refer to the 100 M&Ms listed in Data Set 13 in Appendix B and estimate the probability that when a plain M&M candy is randomly selected, it is one that is blue.b. The Mars Company claims that 24% of its plain M&M candies are blue. Does the estimate from part (a) agree
14. Brand Recognitiona. In a study of brand recognition, 831 consumers knew of Campbell’s Soup, and 18 did not (based on data from Total Research Corporation). Use these results to estimate the probability that a randomly selected consumer will recognize Campbell’s Soup.b. Estimate the
13. Gender Selection In a test of the MicroSort gender-selection technique, results consisted of 295 baby girls and 30 baby boys (based on data from the Genetics & IVF Institute).Based on this result, what is the probability of a girl born to a couple using the MicroSort method? Does it appear that
12. Struck by Lightning In a recent year, 389 of the 281,421,906 people in the United States were struck by lightning. Estimate the probability that a randomly selected person in the United States will be struck by lightning this year.
11. Mendelian Genetics When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of
10. Cell Phones and Brain Cancer In a study of 420,095 cell phone users in Denmark, it was found that 135 developed cancer of the brain or nervous system. Estimate the probability that a randomly selected cell phone user will develop such a cancer. Is the result very different from the probability
9. Gender of Children In this section we gave an example that included a list of the eight outcomes that are possible when a couple has three children. Refer to that list, and find the probability of each event.a. Among three children, there is exactly one girl.b. Among three children, there are
8. Identifying Probability Valuesa. What is the probability of an event that is certain to occur?b. What is the probability of an impossible event?c. A sample space consists of 10 separate events that are equally likely. What is the probability of each?d. On a true false test, what is the
7. Identifying Probability Values Which of the following values cannot be probabilities?
6. Identifying Probability Valuesa. “When flipping a quarter, there is a 50–50 chance that the outcome will be heads.”b. “You have one chance in five of guessing the correct answer.”c. “You have a 1% chance of getting a date with the person who just entered the room.”
5. Identifying Probability Valuesa. “Because you have studied diligently and understand the concepts, you will surely pass the statistics test.”b. “The forecast for tomorrow includes a 10% chance of rain.”c. “You have a snowball’s chance in hell of marrying my daughter.”
4. Subjective Probability Use subjective judgment to estimate the probability that the next time you ride an elevator, it gets stuck between floors.1>2, 1>20,358, 146 Chapter 4 Probability EXAMPLE If you bet $5 on the number 13 in roulette, your probability of winning is and the payoff odds are
3. Probability and Unusual Events A news reporter states that a particular event is unusual because its probability is only 0.001. Is that a correct statement? Why or why not?
2. Probability of Rain When writing about the probability that it will rain in Boston on July 4 of next year, a newspaper reporter states that the probability is because either it will rain or it will not. Is this reasoning correct? Why or why not?
1. Interpreting Probability What does it mean when we say that “the probability of winning the grand prize in the Illinois lottery is 520”? Is such a win unusual?
d. A manufacturer makes fertilizer sticks to be used for growing plants. A manager finds that the amounts of fertilizer placed in the sticks are not very consistent, so that some fertilization lasts longer than claimed, but others don’t last long enough.She wants to improve quality by making the
c. An exit poll is conducted by surveying everyone who leaves the polling booth at 50 randomly selected election precincts. What type of sampling is being used?(Random, stratified, systematic, cluster, convenience)
b. A botanist wants to obtain data about the plants being grown in homes. A sample is obtained by telephoning the first 250 people listed in the local telephone directory, what type of sampling is being used? (Random, stratified, systematic, cluster, convenience)
2.a. A set of data is at the nominal level of measurement and you want to obtain a representative data value. Which of the following is most appropriate: mean, median, mode, or midrange? Why?
1. Tree Measurements Refer to the sample of tree circumferences (in feet) listed in Review Exercise 1.a. Are the given values from a population that is discrete or continuous?b. What is the level of measurement of these values? (Nominal, ordinal, interval, ratio)Q1; Q3; P10.132 Chapter 3 Statistics
7. Estimating Mean and Standard Deviationa. Estimate the mean age of cars driven by students at your college.b. Use the range rule of thumb to make a rough estimate of the standard deviation of the ages of cars driven by students at your college.8. Interpreting Standard Deviation The mean height of
6. Comparing Scores An industrial psychologist for the Citation Corporation develops two different tests to measure job satisfaction. Which score is better: A score of 72 on the management test, which has a mean of 80 and a standard deviation of 12, or a score of 19 on the test for production
5. Boxplot Using the same circumferences listed in Exercise 1, construct a boxplot and identify the values constituting the 5-number summary.
4. Histogram Using the frequency distribution from Exercise 3, construct a histogram and identify the general nature of the distribution (such as uniform, bell-shaped, skewed).
3. Frequency Distribution Using the same tree circumferences listed in Exercise 1, construct a frequency distribution. Use seven classes with 1.0 as the lower limit of the first class, and use a class width of 2.0.
2.a. Using the results from Exercise 1, convert the circumference of 13.7 ft to a z score.b. In the context of these sample data, is the circumference of 13.7 ft “unusual”?Why or why not?c. Using the range rule of thumb, identify any other listed circumferences that are unusual.
1. Tree Heights In a study of the relationship between heights and trunk diameters of trees, botany students collected sample data. Listed below are the tree circumferences(in feet). The data are based on results in “Tree Measurements” by Stanley Rice, American Biology Teacher, Vol. 61, No. 9.
4. Internet Survey An Internet service provider (ISP) conducts an anonymous online survey of its subscribers and 2500 of them respond by reporting the values of the cars that they currently own. Given that the sample size is so large, are the results likely to result in a mean that is fairly close
3. Outlier After 50 credit card holders are randomly selected, the amounts that they currently owe are found. The values of the mean, median, and standard deviation are then determined. An additional amount of $1,000,000 is then included. How much of an effect will this additional amount have on
2. Production Specifications When designing the production procedure for batteries used in heart pacemakers, an engineer specifies that “the batteries must have a mean life greater than 10 years, and the standard deviation of the battery lives can be ignored.”If the mean battery life is greater
1. Center and Variation A quality control engineer redesigns repair procedures so that the standard deviation of the repair times is reduced. Does this imply that the repairs are being done in less time? Why or why not?
15. Mild and Extreme Outliers Some statistics software packages construct boxplots that identify individual mild outliers (often plotted as solid dots) and extreme outliers (often plotted as hollow circles). Mild outliers are below or above by an amount that is greater than IQR but not greater than
14. Outliers Instead of considering a data value to be an outlier if it is “very far away from almost all of the other data values,” consider an outlier to be a value that is above by an amount greater than IQR or below by an amount greater than IQR. Use the data set given below and find the
12. BMI Values Refer to Data Set 1 in Appendix B and use the body mass index (BMI)values of females to find the 5-number summary and construct a boxplot. Do the results appear to be substantially different from those obtained in Exercise 11?
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