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mathematics
statistics

Statistical Reasoning For Everyday Life 4th Edition Jeff Bennett, Bill Briggs, Mario F. Triola - Solutions

The following data sets show the ages of the first seven U.S. Presidents (Washington through Jackson) and seven recent U.S. Presidents (Ford through Obama) at the time of inauguration.a. Find the mean, median, and range for each of the two data sets.b. Give the five-number summary and draw a
The following data sets give the approximate lengths of Beethoven's nine symphonies and Mahler's nine symphonies (in minutes).a. Find the mean, median, and range for each of the two data sets.b. Give the five-number summary and draw a boxplot for each of the two data sets.c. Find the standard
You are in charge of a manufacturing process that produces car batteries that are supposed to provide 12 volts of power. Manufacturing occurs at two different sites. The first site produces batteries with a mean of 12.1 volts and a standard deviation of 0.5 volt, while the second site produces
The book Investments, by Zvi Bodie, Alex Kane, and Alan Marcus, claims that the annual percentage returns for investment portfolios with a single stock have a standard deviation of 0.55, while the annual percentage returns for portfolios with 32 stocks have a standard deviation of 0.325. Explain
Jennifer received an SAT score that was equal to the first quartile and the 35th percentile. Decide whether the statement make sense or not? Explain clearly.
If the range of salaries paid to baseball players in the American League is less than the range of salaries paid to baseball players in the National League, then the American League salaries must have a smaller standard deviation than the National League salaries. Decide whether the statement make
A baseball player is given a test for banned substances. For this test, what is a false positive? What is a false negative? What is a true positive? What is a true negative?
The table below shows eighth-grade mathematics test scores in Nebraska and New Jersey. The scores are separated according to the race of the student. Also shown are the state averages for all races.a. Which state had the higher scores in both racial categories? Which state had the higher overall
Consider the following table comparing the grade point averages (GPAs) and mathematics SAT scores of high school students in 1988 and 1998 (before the SAT test format was revised).a. In general terms, how did the SAT scores of the students in the five grade categories change between 1988 and
The following table shows deaths due to tuberculosis (TB) in New York City and Richmond, Virginia, in 1910.a. Compute the death rates for whites, nonwhites, and all residents in New York City.b. Compute the death rates for whites, nonwhites, and all residents in Richmond.c. Explain why this is an
Two cross-country running teams participated in a (hypothetical) study in which a fraction of each team used weight training to supplement a running workout. The remaining runners did not use weight training. At the end of the season, the mean improvement in race times (in seconds) was recorded in
Consider the following (hypothetical) basketball records for Spelman and Morehouse Colleges.a. Give numerical evidence to support the claim that Spelman College has a better team than Morehouse College. b. Give numerical evidence to support the claim that Morehouse College has a better team than
Two drugs, A and B, were tested on a total of 2,000 patients, half of whom were women and half of whom were men. Drug A was given to 900 patients and Drug B to 1,100 patients. The results appear in the table below.a. Give numerical evidence to support the claim that Drug B is more effective than
The results in the table below are from experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute). In each case, it was known whether the subject lied, so the table indicates when the polygraph test was
Suppose a test for a disease is 80% accurate for those who have the disease (true positives) and 80% accurate for those who do not have the disease (true negatives). Within a sample of 4,000 patients, the incidence rate of the disease matches the national average, which is 1.5%.a. Of those with the
A company decided to expand, so it opened a factory, generating 455 jobs. For the 70 white-collar positions, 200 males and 200 females applied. Of the females who applied, 20% were hired, while only 15% of the males were hired. Of the 400 males applying for the blue-collar positions, 75% were
A company runs two trials of two treatments for an illness. In the first trial, Treatment A cures 20% of the cases (40 out of 200) and Treatment B cures 15% of the cases (30 out of 200). In the second trial, Treatment A cures 85% of the cases (85 out of 100) and Treatment B cures 75% of the cases
The New York State Department of Health estimates a 10% rate of HIV for the at-risk population and a 0.3% rate for the general population. Tests for HIV are 95% accurate in detecting both true negatives and true positives. Random selection and testing of 5,000 at-risk people and 20,000 people from
If a drug test is 90% accurate, it follows that 90% of those who test positive are actual drug users. Decide whether the statement make sense or not? Explain clearly.
The table below shows the batting records of two baseball players in the first half (first 81 games) and last half of a season.Who had the higher batting average in the first half of the season? Who had the higher batting average in the second half? Who had the higher overall batting average?
For each of the following situations, state whether the distribution of values is likely to be a normal distribution. Give a brief explanation justifying your choice. a. Numbers resulting from spins of a roulette wheel. (There are 38 equally likely slots with numbers 0, 00, 1, 2, 3, ...,36.) b.
The College of Portland uses a diagnostics test to correctly place students in math courses. Scores on the test are normally distributed with a mean of 400 and a standard deviation of 50.1. Using the 68-95-99.7 rule, find the percentage of scores within 50 of the mean of 400.2. Using the 68-95-99.7
Assume that body temperatures of healthy adults are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F (based on data from University of Maryland researchers).a. If you have a body temperature of 99.00°F, what is your percentile score?b. Convert 99.00°F to a standard
The exact weights of a random sample of quarters manufactured in 2012 by the U.S. Mint. State whether you expect it to be normally distributed. Explain your reasoning.
The incomes of randomly selected adults in the United States. State whether you expect it to be normally distributed. Explain your reasoning.
All of the SAT scores from last year. State whether you expect it to be normally distributed. Explain your reasoning.
The measured white blood cell counts of 500 randomly selected adult women. State whether you expect it to be normally distributed. Explain your reasoning.
The amounts of the fines from parking tickets found on a random sample of 1,000 parked cars. State whether you expect it to be normally distributed. Explain your reasoning.
Figure 5.8 shows a histogram for the lengths of 60 movies. The mean movie length is 110.5 minutes. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not?
Figure 5.11 shows a histogram for the weights of 30 randomly selected aspirin tablets. The mean weight is 665.4 milligrams. Is this distribution close to normal? Should this variable have a normal distribution? Why or why not?
Consider the graph of the normal distribution in Figure 5.12, which gives relative frequencies in a distribution of men's heights. The distribution has a mean of 69.6 inches and a standard deviation of 2.8 inches.a. What is the total area under the curve?b. Estimate (using area) the relative
Consider the graph of the normal distribution in Figure 5.13, which shows the relative frequencies in a distribution of IQ scores. The distribution has a mean of 100 and a standard deviation of 16.a. What is the total area under the curve? b. Estimate (using area) the relative frequency of values
The mean of a normally distributed set of IQ scores is 100, and 60% of the scores are over 105. Decide whether the statement make sense or not? Explain clearly.
Assume the resting pulse rates for a sample of individuals are normally distributed with a mean of 70 and a standard deviation of 15. Use the 68-95-99.7 rule to find the following quantities.a. Percentage of pulse rates less than 70b. Percentage of pulse rates greater than 55c. Percentage of pulse
In a study of facial behavior, people in a control group are timed for eye contact in a 5-minute period. Their times are normally distributed with a mean of 184.0 seconds and a standard deviation of 55.0 seconds (based on data from "Ethological Study of Facial Behavior in Non-paranoid and Paranoid
When designing the placement of a CD player in a new model car, engineers must consider the forward grip reach of the driver. Women have forward grip reaches that are normally distributed with a mean of 27.0 inches and a standard deviation of 1.3 inches (based on anthropometric survey data from
Percentage of scores between 68 and 132 The normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 16. Use Table 5.1 (on page 175) to find the indicated quantities, for standard scores above 3.5, use a percentile of 99.99%; for all standard scores below —3.5, use a
Percentage of scores between 52 and 116 The normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 16. Use Table 5.1 (on page 175) to find the indicated quantities, for standard scores above 3.5, use a percentile of 99.99%; for all standard scores below —3.5, use a
Percentage of scores between 76 and 108 The normal distribution of IQ scores, which has a mean of 100 and a standard deviation of 16. Use Table 5.1 (on page 175) to find the indicated quantities, for standard scores above 3.5, use a percentile of 99.99%; for all standard scores below —3.5, use a
The percentage of heights between 156 centimeters and 168 centimeters Use the normal distribution of heights of adult women, which has a mean of 162 centimeters and a standard deviation of 6 centimeters. Use table 5.1 to find the indicated quantities.
The percentage of heights between 159 centimeters and 165 centimeters Use the normal distribution of heights of adult women, which has a mean of 162 centimeters and a standard deviation of 6 centimeters. Use table 5.1 to find the indicated quantities.
Consider the following table, showing the official mean weight and estimated standard deviation for five U.S. coins. Suppose a vending machine is designed to reject all coins with weights more than 2 standard deviations above or below the mean. For each coin, find the range of weights that is
Lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.a. What is the percentage of pregnancies that last less than 250 days?b. What is the percentage of pregnancies that last more than 300 days?c. If a birth is considered premature if the
Based on data from the College Board, SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325.a. Find the percentage of SAT scores greater than 2000.b. Find the percentage of SAT scores less than 1500.c. Find the percentage of SAT scores between 1600 and 2100.
Table 5.1 includes standard scores and percentiles. Can a z-score be a negative value? Can a percentile be a negative value? Explain.
Assume that the scores on the Graduate Record Exam (GRE) are normally distributed with a mean of 497 and a standard deviation of 115.a. A graduate school requires a GRE score of 650 for admission. To what percentile does this correspond?b. A graduate school requires a GRE score in the 95th
Researchers for a manufacturer of barometers (devices to measure atmospheric pressure) read each of 50 barometers at the same time of day. The mean of the readings is 30.4 (inches of mercury) with a standard deviation of 0.23 inch, and the readings appear to be normally distributed.a. What
At the district spelling bee, the 60 girls have a mean score of 71 points with a standard deviation of 6, while the 50 boys have a mean score of 66 points with a standard deviation of 5 points. Those students with a score greater than 75 are eligible to go to the state spelling bee. What percentage
According to data from the National Health Survey, the heights of adult men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that men have heights between 64 inches and 78 inches. What percentage of American men are eligible
Based on a random sample of movie lengths, the mean length is 110.5 minutes with a standard deviation of 22.4 minutes. Assume that movie lengths are normally distributed.a. What fraction of movies are more than 2 hours long?b. What fraction of movies are less than lj hours long?c. What is the
Scores on a statistics test are normally distributed with a mean of 75 and a standard deviation of 75. Decide whether the statement does make sense or not? Explain clearly.
A test of depth perception is designed so that scores are normally distributed with a mean of 50 and a standard deviation of 10. Use the 68-95-99.7 rule to find the following values.a. Percentage of scores less than 50b. Percentage of scores less than 60c. Percentage of scores greater than 70d.
In each drawing for the Texas Pick 3 lottery, 3 digits between 0 and 9 (inclusive) are randomly selected. What is the distribution of the selected digits? If the mean is calculated for each drawing, can the distribution of the sample means be treated as a normal distribution?
What percentage of individual men have weights greater than 167 lb? If samples of 100 men are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are greater than 167 lb? Assume that weights of men are normally distributed with a mean of 170 lb and
What percentage of individual men have weights between 164 lb and 176 lb? If samples of 100 men are randomly selected and the mean weight is computed for each sample, what percentage of sample means is between 164 lb and 176 lb? Assume that weights of men are normally distributed with a mean of 170
What percentage of individual men have weights between 176 lb and 185 lb? If samples of 25 men are randomly selected and the mean weight is computed for each sample, what percentage of sample means is between 176 lb and 185 lb? Assume that weights of men are normally distributed with a mean of 170
Assume that cans of cola are filled so that the actual amounts are normally distributed with a mean of 12.00 ounces and a standard deviation of 0.11 ounce.a. What is the likelihood that a sample of 36 cans will have a mean amount of at least 12.05 ounces?b. Given the result in part a, is it
An aircraft strobe light is designed so that the times between flashes are normally distributed with a mean of 3.00 seconds and a standard deviation of 0.40 second.a. What is the likelihood that an individual time is greater than 4.00 seconds?b. What is the likelihood that the mean for 60 randomly
Engineers must consider the breadths of male heads when designing motorcycle helmets for men. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of l .0 inch (based on anthropometric survey data from Gordon, Churchill et al.).a. If one male is
In planning for hot water requirements, the manager of the Luxurion Hotel finds that guests spend a mean of 11.4 minutes each day in the shower (based on data from the Opinion Research Corporation). Assume that the shower times are normally distributed with a standard deviation of 2.7 minutes.a.
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 pounds and 211 pounds. The population of women has normally distributed
M&M plain candies have weights that are normally distributed with a mean weight of 0.8565 gram and a standard deviation of 0.0518 gram (based on measurements from one of the authors). A random sample of 100 M&M candies is obtained from a package containing 465 candies; the package label
Currently, quarters have weights that are normally distributed with a mean of 5.670 grams and a standard deviation of 0.062 gram. A vending machine is configured to accept only those quarters with weights between 5.550 grams and 5.790 grams.a. If 280 different quarters are inserted into the vending
Federal Aviation Administration rules require airlines to estimate the weight of a passenger as 195 pounds, including carry-on baggage. Men have weights (without baggage) that are normally distributed with a mean of 172 pounds and a standard deviation of 29 pounds.a. If one adult male is randomly
In designing new desks for an incoming class of 25 kindergarten girls, an important characteristic of the desks is that they must accommodate the sitting heights of those students. (The sitting height is the height of a seated student measured from the bottom of the feet to the top of the knee.)
Systolic blood pressure for women between the ages of 18 and 24 is normally distributed with a mean of 114.8 (millimeters of mercury) and a standard deviation of 13.1.a. What is the likelihood that an individual woman has a blood pressure above 125?b. Suppose a random sample of n = 300 women is
For each of the following situations, state whether the distribution of values is likely to be a normal distribution. Give a brief explanation justifying your choice. a. Numbers resulting from spins of a roulette wheel. (There are 38 equally likely slots with numbers 0, 00, 1, 2, 3... 36.) b.
The College of Portland uses a diagnostics test to correctly place students in math courses. Scores on the test are normally distributed with a mean of 400 and a standard deviation of 50. a. Using the 68-95-99.7 rule, find the percentage of scores within 50 of the mean of 400. b. Using the
Assume that body temperatures of healthy adults are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F (based on data from University of Maryland researchers).a. If you have a body temperature of 99.00°F, what is your percentile score?b. Convert 99.00°F to a standard
IQ scores are normally distributed with a mean of 100 and a standard deviation of 16. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample.a. If the sample size is n = 64, find the mean and standard deviation of the
Based on data from the College Board, assume that SAT scores are normally distributed with a mean of 1518 and a standard deviation of 325. Assume that many samples of size n are taken from a large population of students and the mean SAT score is computed for each sample.a. If the sample size is n =
Rolling a fair 12-sided die produces a uniformly distributed set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Assume that n 12-sided dice are rolled many times and the mean of the n outcomes is computed each time.a. Find the mean and standard deviation of the
Rolling a fair 10-sided die produces a uniformly distributed set of numbers between 1 and 10 with a mean of 5.5 and a standard deviation of 2.872. Assume that n 10-sided dice are rolled many times and the mean of the n outcomes is computed each time.a. Find the mean and standard deviation of the
What percentage of individual men have weights less than 185 lb? If samples of 36 men are randomly selected and the mean weight is computed for each sample, what percentage of the sample means are less than 185 lb? Assume that weights of men are normally distributed with a mean of 170 lb and a
For a recent year, the fatality rate from motor vehicle crashes was reported as 15.2 per 100,000 population. a. What is the probability that a randomly selected person will die this year as a result of a motor vehicle crash? b. If two people are randomly selected, find the probability that they
If one of the subjects is randomly selected, find the probability of selecting someone who had a head injury or wore a helmet.
If one of the subjects is randomly selected, find the probability of selecting someone who did not wear a helmet or was not injured.
If two different study subjects are randomly selected, find the probability that they both wore helmets.
The Binary Computer Company manufactures computer chips used in DVD players. Those chips are made with a 27% yield, meaning that 27% of them are good and the others are defective.a. If one chip is randomly selected, find the probability that it is not good.b. If two chips are randomly selected,
In an experiment testing a method of gender selection intended to increase the likelihood that a baby is a girl, 1,000 couples give birth to 501 girls and 499 boys. A company representative argues that this is evidence that the method is effective, because the probability of getting 501 girls in
In 6 rolls of a six-sided die, the outcome of 6 never occurs.
A commuter enters a New York City subway car near Times Square and finds that it is occupied by 50 men, all of whom are bald.
In a clinical trial of a new drug intended to treat allergies, 5 of the 80 subjects in the treatment group experienced headaches, and 8 of the 160 subjects in the control group experienced headaches.
An experiment was conducted to determine whether there is a difference between the success rates from treating carpal tunnel syndrome with surgery and with splinting. The success rate for 73 patients treated with surgery was 92%, and the success rate for 83 patients treated with splints was 72%
The Genetics and IVF Institute conducted a clinical trial of its method for gender selection. The latest actual results showed that among 945 babies born to couples using the XSORT method of gender selection, 879 were girls.
Does the term statistical significance refer to results that are significant in the sense that they have great importance? Explain.
In a randomized controlled trial in Kenya, insecticide-treated bednets were tested as a way to reduce malaria. Among 343 infants who used the bednets, 15 developed malaria. Among 294 infants not using bednets, 27 developed malaria (based on data from "Sustainability of Reductions in Malaria
In a study by researchers at the University of Maryland, the body temperatures of 106 individuals were measured; the mean for the sample was 98.20°F. It is commonly believed that the mean body temperature is 98.60°F. The difference between the sample mean and the accepted value is significant at
In a study of children injured in automobile crashes (American Journal of Public Health, Vol. 82, No. 3), those wearing seat belts had a mean stay of 0.83 day in an intensive care unit. Those not wearing seat belts had a mean stay of 1.39 days. The difference in means between the two groups is
If a particular result is statistically significant at the 0.05 level, must it also be statistically significant at the 0.01 level? Why or why not?
If a particular result is statistically significant at the 0.01 level, must it also be statistically significant at the 0.05 level? Why or why not? Does It Make Sense? For Exercises 5-8, decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).
The rate of unemployment has statistical significance because it has such a strong effect on the economy.
In an experiment testing a method of gender selection, 1,000 couples give birth to 550 girls and 450 boys. Because the probability of getting such extreme results by chance is only 0.0009, the results are statistically significant.
In a clinical trial of a treatment for reducing back pain, the difference between the treatment group and the control group (with no treatment) was found to be statistically significant. This means that the treatment will definitely ease back pain for everyone.
If A denotes the event that you answer a particular true/false test question correctly, what do each of the following represent: P(A), P (notA), P(A), and what are their values?
Rolling a die and getting an outcome that is greater than 2.
Rolling a pair of dice and getting an outcome (sum) of 12. Complementary Events. Exercises 19-26 involve complementary events. In each exercise, find the probability of the given event. State any assumptions that you use.
A student reasons that there is a probability of 1/2 that there is life on Neptune, because there are two possible events: There is life or there is not life. Is this reasoning correct? Why or why not?
A bag contains 10 red M&Ms, 15 blue M&Ms, and 20 yellow M&Ms. What is the probability of drawing a red M&M? A blue M&M? A yellow M&M? Something besides a yellow M&M?
Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. What is the probability that the family has each of the following?a. Three girlsb. Two boys and a girlc. A girl, a boy, and a boy, in that orderd. At least one girle. At least two boys

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