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Elementary Statistics 10th Edition Mario F. Triola - Solutions
2. Left-Handedness According to data from the American Medical Association, 10% of us are left-handed.a. If three people are randomly selected, find the probability that they are all lefthanded.b. If three people are randomly selected, find the probability that at least one of them is
1. Carbohydrates in Food Some standard food items are randomly selected and the carbohydrate contents (in grams) are measured with the results listed below (based on data from the U.S. Department of Agriculture). (The items are 12 oz of regular coffee, one cup of whole milk with 3.3% fat, one egg,
6. Testing for Normality Listed below are the lengths of time (in days) that the New York State budget has been late for each of 19 consecutive and recent years. Do those lengths of time appear to come from a population that has a normal distribution? Why or why not?4 4 10 19 18 48 64 1 4 68 67 103
5. Gender Discrimination When several women are not hired at the Telektronics Company, they do some research and find that among the many people who applied, 30% were women. However, the 20 people who were hired consist of only 3 women and 17 men. Find the probability of randomly selecting 20
4. Detecting Gender Bias in a Test Question When analyzing one particular question on an IQ test, it is found that among the 20 people who answered incorrectly, 18 are women. Given that the test was given to the same number of men and women, all carefully chosen so that they have the same
3. High Cholesterol Levels The serum cholesterol levels in men aged 18–24 are normally distributed with a mean of 178.1 and a standard deviation of 40.7. Units are in mg 100 mL, and the data are based on the National Health Survey.a. If one man aged 18–24 is randomly selected, find the
2. Boston Beanstalk Club The Boston Beanstalk Club has a minimum height requirement of 74 in. for men. Heights of men are normally distributed with a mean of 69.0 in.and a standard deviation of 2.8 in. (based on data from the National Health Survey).a. What percentage of men meet the minimum height
1. Weighing Errors A scale is designed so that when items are weighed, the errors in the indicated weights are normally distributed with a mean of 0 g and a standard deviation of 1 g. (If the scale reading is too low, the error is negative. If the scale reading is too high, the error is
4. Central Limit Theorem What does the central limit theorem tell us?
3. Simple Random Sample A researcher has collected a large sample of IQ scores from friends and relatives. He claims that because his sample is large and the distribution of his sample scores is very close to the bell shape of a normal distribution, his sample is representative of the population.
2. Distribution of Sample Means A process consists of randomly selecting 250 adults, measuring the grip strength (right hand only), then finding the sample mean. Assuming that this process is repeated many times, what important fact do we know about the distribution of the resulting sample means?
1. Normal Distribution What is a normal distribution? What is a standard normal distribution?
37. Normal Approximation Required This section included the statement that “In reality, almost all practical applications of the binomial probability distribution can now be handled well with software or a TI-83 84 Plus calculator.” Using a specific software package or a TI-83 84 Plus
36. Overbooking Flights Vertigo Airlines works only with advance reservations and experiences a 7% rate of no-shows. How many reservations could be accepted for an airliner with a capacity of 250 if there is at least a 0.95 probability that all reservation holders who show will be accommodated?
35. Joltin’ Joe Assume that a baseball player hits .350, so his probability of a hit is 0.350.(Ignore the complications caused by walks.) Also assume that his hitting attempts are independent of each other.a. Find the probability of at least 1 hit in 4 tries in 1 game.b. Assuming that this batter
34. Replacement of TVs Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 year (based on data from “Getting Things Fixed,” Consumer Reports). Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have
33. Winning at Roulette Marc Taylor plans to place 200 bets of $1 each on the number 7 at roulette. A win pays off with odds of 35:1 and, on any one spin, there is a probability of 1 38 that 7 will be the winning number. Among the 200 bets, what is the minimum number of wins needed for Marc to make
32. Detecting Fraud When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of amounts on checks from companies that were suspected of fraud. Among 784 checks, 479 had amounts with leading digits of 5, but checks issued in the normal course of honest
31. Detecting Credit Card Fraud The Dynamic Credit company issues credit cards and uses software to detect fraud. After tracking the spending habits of one consumer, it is found that charges over $100 constitute 35.8% of the credit transactions. Among 30 charges made this month, 18 involve totals
30. Bias in Jury Selection In Orange County, 12% of those eligible for jury duty are lefthanded.Among 250 people selected for jury duty, 25 (or 10%) are lefties. Find the probability of getting at most 25 lefties asssuming that they are chosen with a process designed to yield a 12% rate of lefties.
29. Cloning Survey 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 news reporter wants to determine whether these
28. Acceptance Sampling Some companies monitor quality by using a method of acceptance sampling, whereby an entire batch of items is rejected if a random sample of a 6-6 Normal as Approximation to Binomial 301 particular size includes more than some specified number of defects. The Dayton Machine
27. Blood Group Forty-five percent of us have Group O blood, according to data provided by the Greater New York Blood Program. Providence Memorial Hospital is conducting a blood drive because its supply of Group O blood is low, and it needs 177 donors of Group O blood. If 400 volunteers donate
26. M&M Candies: Are 20% Orange? According to Mars (the candy company, not the planet), 20% of M&M plain candies are orange. Data Set 13 in Appendix B shows that among 100 M&Ms chosen, 25 are orange. Assuming that the claimed orange M&Ms rate of 20% is correct, estimate the probability of randomly
25. Identifying Gender Discrimination After being rejected for employment, Kim Kelly learns that the Bellevue Advertising Company has hired only 21 women among its last 62 new employees. She also learns that the pool of applicants is very large, with an equal number of qualified men and women. Help
24. Overbooking Flights Air America is considering a new policy of booking as many as 400 persons on an airplane that can seat only 350. (Past studies have revealed that only 85% of the booked passengers actually arrive for the flight.) Estimate the probability that if Air America books 400
23. 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. Assuming that cell phones have no effect, there is a 0.000340 probability of a person developing cancer of the brain or nervous system. We
22. Cholesterol Reducing Drug The probability of flu symptoms for a person not receiving any treatment is 0.019. In a clinical trial of Lipitor, a common drug used to lower cholesterol, 863 patients were given a treatment of 10-mg atorvastatin tablets, and 19 of those patients experienced flu
21. Mendel’s Hybridization Experiment 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% (or 145) of the 580 offspring peas were expected to have yellow pods. Instead of getting 145
20. TV Advertising Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the
19. Voters Lying? In a survey of 1002 people, 701 said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote. Given that 61% of eligible voters actually did vote, find the probability that among
18. Probability of at Least 42 Girls Assuming that boys and girls are equally likely, estimate the probability of getting at least 42 girls in 64 births. Is it unusual to get at least 42 girls in 64 births?
17. Probability of More Than 36 Girls Assuming that boys and girls are equally likely, estimate the probability of getting more than 36 girls in 64 births. Is it unusual to get more than 36 girls in 64 births?
4. Interpreting Binomial Probability In a test of a method of gender selection, 80 couples are given a treatment designed to increase the likelihood that a baby will be a girl. There were 47 girls among the 80 babies born. If the gender-selection method has no effect, the probability of getting
3. Distribution of Sample Proportions The Newport Bottling plant produces bottles of cola that are packaged in six-packs. The probability of a defective bottle is 0.001. Can we approximate the distribution of defects in six-packs as a normal distribution? Why or why not?
2. Continuity Correction The Wechsler test is used to measure IQ scores. It is designed so that the mean is 100 and the standard deviation is 16. It is known that IQ scores have a normal distribution. Assume that we want to find the probability that a randomly selected person has an IQ equal to
1. Distribution of Sample Proportions Consider a study in which we obtain records from the next 50 babies that are born, then compute the proportion of girls in this sample. Assume that this study is repeated many times, and the sample proportions are used to construct a histogram. What is the
23. Population Parameters A population consists of these values: 2, 3, 6, 8, 11, 18.a. Find and .b. List all samples of size n 2 that can be obtained without replacement.c. Find the population of all values of by finding the mean of each sample from part(b).d. Find the mean and standard deviation
22. Correcting for a Finite Population The Boston Women’s Club needs an elevator limited to 8 passengers. The club has 120 women members with weights that approximate a normal distribution with a mean of 143 lb and a standard deviation of 29 lb.(Hint: See the discussion of the finite population
21. Seating Design You need to build a bench that will seat 18 male college football players, and you must first determine the length of the bench. Men have hip breadths that are normally distributed with a mean of 14.4 in. and a standard deviation of 1.0 in.a. What is the minimum length of the
20. Aircraft Safety Standards Under older Federal Aviation Administration rules, airlines had to estimate the weight of a passenger as 185 pounds. (That amount is for an adult traveling in winter, and it includes 20 pounds of carry-on baggage.) Current rules require an estimate of 195 pounds. Men
19. Vending Machines Currently, quarters have weights that are normally distributed with a mean of 5.670 g and a standard deviation of 0.062 g. A vending machine is configured to accept only those quarters with weights between 5.550 g and 5.790 g.a. If 280 different quarters are inserted into the
18. Labeling of M&M Packages M&M plain candies have a mean weight of 0.8565 g and a standard deviation of 0.0518 g (based on Data Set 13 in Appendix B). The M&M candies used in Data Set 13 came from a package containing 465 candies, and the package label stated that the net weight is 396.9 g. (If
17. Redesign of Ejection Seats When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been designed for men only. The ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. The population of women has
16. Staying Out of Hot Water In planning for hot water requirements, the manager of the Luxurion Hotel finds that guests spend a mean of 11.4 min each day in the shower(based on data from the Opinion Research Corporation). Assume that the shower times are normally distributed with a standard
d. If a physician is given a report stating that 4 women have a mean systolic blood pressure below 140, can she conclude that none of the women have hypertension(with a blood pressure greater than 140)?
b. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.c. Given that part(b) involves a sample size that is not larger than 30, why can the central limit theorem be used?
a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 140.
15. Blood Pressure For women aged 18–24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140.
b. The Safeguard Helmet company plans an initial production run of 100 helmets.Find the probability that 100 randomly selected men have a mean head breadth less than 6.2 in.c. The production manager sees the result from part(b) and reasons that all helmets should be made for men with head breadths
a. If one male is randomly selected, find the probability that his head breadth is less than 6.2 in.
14. Designing Motorcycle Helmets Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in. (based on anthropometric survey data from Gordon, Churchill, et al.).
13. Designing Strobe Lights An aircraft strobe light is designed so that the times between flashes are normally distributed with a mean of 3.00 s and a standard deviation of 0.40 s.a. Find the probability that an individual time is greater than 4.00 s.b. Find the probability that the mean for 60
d. If the random sample of 16 men does result in a mean score of 590, is there strong evidence to support the claim that the course is actually effective? Why or why not?
c. In finding the probability for part(b), why can the central limit theorem be used even though the sample size does not exceed 30?
b. If 16 of the men are randomly selected, find the probability that their mean score is at least 590.
a. If 1 of the men is randomly selected, find the probability that his score is at least 590.
12. Coaching for the SAT Scores for men on the verbal portion of the SAT-I test are normally distributed with a mean of 509 and a standard deviation of 112 (based on data>6-5 The Central Limit Theorem 289 from the College Board). Randomly selected men are given the Columbia Review Course before
11. Amounts of Coke Assume that cans of Coke are filled so that the actual amounts have a mean of 12.00 oz and a standard deviation of 0.11 oz.a. Find the probability that a sample of 36 cans will have a mean amount of at least 12.19 oz, as in Data Set 12 in Appendix B.b. Based on the result from
10. Casino Buses The new Lucky Lady Casino wants to increase revenue by providing buses that can transport gamblers from other cities. Research shows that these gamblers tend to be older, they tend to play slot machines only, and they have losses with a mean of $182 and a standard deviation of
b. Find the probability that 12 randomly selected men will have a mean that is greater than 167 pounds (so that their total weight is greater than the gondola maximum capacity of 2004 lb).c. Does the gondola appear to have the correct weight limit? Why or why not?
a. Find the probability that if an individual man is randomly selected, his weight will be greater than 167 pounds.
9. Gondola Safety A ski gondola in Vail, Colorado, carries skiers to the top of a mountain.It bears a plaque stating that the maximum capacity is 12 people or 2004 pounds.That capacity will be exceeded if 12 people have weights with a mean greater than 2004 12 167 pounds. Because men tend to
c. Why can the central limit theorem be used in part (b), even though the sample size does not exceed 30?
b. If 16 women are randomly selected, find the probability that they have a mean height between 60 in. and 65 in.
8.a. If 1 woman is randomly selected, find the probability that her height is between 60 in. and 65 in.
c. Why can the central limit theorem be used in part (b), even though the sample size does not exceed 30?
b. If 9 women are randomly selected, find the probability that they have a mean height between 63.5 in. and 64.5 in.
7.a. If 1 woman is randomly selected, find the probability that her height is between 63.5 in. and 64.5 in.
b. If 100 women are randomly selected, find the probability that they have a mean height greater than 63 in.
6.a. If 1 woman is randomly selected, find the probability that her height is greater than 63 in.
4. Convenience Sample Because a statistics student waited until the last minute to do a project, she has only enough time to collect heights from female friends and female relatives. She then calculates the mean height of the females in her sample. Assuming that females have heights that are
3. Notation Large (n 30) samples are randomly selected from a population with mean and standard deviation . What notation is used for the mean of the population consisting of all sample means? What notation is used for the standard deviation of the population consisting of all sample means?
2. Small Sample If selecting samples of size n 2 from a population with a known mean and standard deviation, what requirement must be satisfied in order to assume that the distribution of the sample means is a normal distribution?
1. Standard Error of the Mean What is the standard error of the mean?
15. Using a Formula to Describe a Sampling Distribution See the first example in this section, which includes a table and graph to describe the sampling distribution of the proportions of girls from two births. Consider the formula shown below, and evaluate that formula using sample proportions x
14. Median and Moons of Jupiter Jupiter has 4 large moons and 12 small moons. The 4 large moons have these orbit times (in days): 1.8 (Io), 3.6 (Europa), 7.2 (Ganymede), and 16.7(Callisto). Assume that two of these values are randomly selected with replacement.a. After identifying the 16 different
13. Ranks of Olympic Triathlon Competitors U.S. women competed in the triathlon in the Olympic games held in Athens, and their final rankings were 3, 9, and 23. Assume that samples of size 2 are randomly selected with replacement.a. Use a table to describe the sampling distribution of the sample
12. Quality Control After constructing a new manufacturing machine, 5 prototype car headlights are produced and it is found that 2 are defective (D) and 3 are acceptable (A).Assume that two headlights are randomly selected with replacement from this population.a. After identifying the 25 different
11. Genetics A genetics experiment involves a population of fruit flies consisting of 1 male named Mike and 3 females named Anna, Barbara, and Chris. Assume that two fruit flies are randomly selected with replacement.a. After listing the 16 different possible samples, find the proportion of females
10. Military Presidents Here is the population of all five U.S. presidents who had professions in the military, along with their ages at inauguration: Eisenhower (62), Grant(46), Harrison (68), Taylor (64), and Washington (57). Assume that samples of size 2 are randomly selected with replacement
9. Wealthiest People The assets (in billions of dollars) of the five wealthiest people in the United States are 47 (Bill Gates), 43 (Warren Buffet), 21 (Paul Allen), 20 (Alice Walton), and 20 (Helen Walton). Assume that samples of size 2 are randomly selected with replacement from this population
8. Telemarketing Here are the numbers of sales per day that were made by Kim Ryan, a courteous telemarketer who worked four days before being fired: 1, 11, 9, 3. Assume that samples of size 2 are randomly selected with replacement from this population of four values.a. List the 16 different
7. Phone Center The Nome Ice Company was in business for only three days (guess why). Here are the numbers of phone calls received on each of those days: 10, 6, 5.Assume that samples of size 2 are randomly selected with replacement from this population of three values.a. List the 9 different
6. Sampling Distribution of Body Temperatures Data Set 2 in Appendix B includes a sample of 106 body temperatures of adults. If we were to construct a histogram to depict the shape of the distribution of that sample, would that histogram show the shape of a sampling distribution of sample means?
5. Survey of Voters Based on a random sample of n 400 voters, the NBC news division predicts that the Democratic candidate for the presidency will get 49% of the vote, but she actually gets 51%. Should we conclude that the survey was done incorrectly?Why or why not?
4. Sampling with Replacement Give at least one reason why statistical methods tend to be based on the assumption that sampling is conducted with replacement, instead of without replacement.
3. Unbiased Estimators Which of the following statistics are unbiased estimators?a. Sample mean used to estimate a population meanb. Sample median used to estimate a population medianc. Sample proportion used to estimate a population proportiond. Sample variance used to estimate a population
2. Unbiased Estimator What does it mean when we say that sample means “target” the population mean, or that the sample mean is an unbiased estimator of the population mean?
1. Sampling Distribution Use your own words to answer this question: “What is a sampling distribution?”
30. SAT and ACT Tests Scores by women on the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the two tests use different scales to
29. Curving Test Scores A statistics professor gives a test and finds that the scores are normally distributed with a mean of 25 and a standard deviation of 5. She plans to curve the scores.a. If she curves by adding 50 to each grade, what is the new mean? What is the new standard deviation?b. Is
28. Using Continuity Correction There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values. In such cases, we can use this continuity correction: Represent each whole number by the interval extending from 0.5 below
27. Units of Measurement Heights of women are normally distributed.a. If heights of individual women are expressed in units of inches, what are the units used for the z scores that correspond to individual heights?b. If heights of all women are converted to z scores, what are the mean, standard
25. Appendix B Data Set: Systolic Blood Pressure Refer to Data Set 1 in Appendix B and use the systolic blood pressure levels for males.a. Using the systolic blood pressure levels for males, find the mean, standard deviation, and verify that the data have a distribution that is roughly normal.b.
24. Sitting Distance A common design requirement is that an item (such as an aircraft or theater seat) must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. If this requirement is adopted, what is the minimum sitting distance and what is the
23. Designing Helmets Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 in. and a standard deviation of 1.0 in. (based on anthropometric survey data from Gordon, Churchill, et al.). Due to
22. Hip Breadths and Aircraft Seats Engineers want to design seats in commercial aircraft so that they are wide enough to fit 98% of all males. (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a
21. Lengths of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.a. One classical use of the normal distribution is inspired by a letter to “Dear Abby”in which a wife claimed to have given birth 308 days after a brief
20. Body Temperatures Based on the sample results in Data Set 2 of Appendix B, assume that human body temperatures are normally distributed with a mean of 98.20F and a standard deviation of 0.62F.a. Bellevue Hospital in New York City uses 100.6F as the lowest temperature considered to be a
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