Questions and Answers of Practice of Statistics

The following figure is a Normal probability plot of the emissions of carbon dioxide (CO2) per person in 48 countries.15 Use the graph to determine if this distribution of CO2 emissions is
A carpenter sells handmade wooden benches at a craft fair every week. Over the past year, the carpenter has varied the price of the benches from $80 to $120 and recorded the average weekly profit he
Marc and Rob are both high school English teachers. Students think that Rob is a harder grader, so Rob and Marc decide to grade the same 10 essays and see how their scores compare. The correlation is
A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, “The evidence indicates that the correlation between the research
Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and
Refer to Exercise 20.a. Explain why it isn’t correct to say that the correlation is 0.86 g/kg.b. What would happen to the correlation if the variables were reversed on the scatterplot? Explain your
Archaeopteryx is an extinct beast that had feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known to exist today. Because these specimens differ
Refer to Exercise 19.a. Explain why it isn’t correct to say that the correlation is 0.87 mg/cal.b. What would happen to the correlation if the variables were reversed on the scatterplot? Explain
A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining dorm rooms. Then she measures the next man
The following scatterplot plots the average brain weight (in grams) versus average body weight (in kilograms) for 96 species of mammals. There are many small mammals whose points overlap at the lower
The following scatterplot shows the calories and salt content (measured in milligrams of sodium) in 17 brands of meat hot dogs.a. The correlation for these data is r = 0.87. Interpret this value.b.
Refer to Exercise 16. Does the fact that r = 0.45 suggest that making an infant cry will increase his or her IQ later in life? Explain your reasoning.Exercise 16.Infants who cry easily may be more
Here is a scatterplot showing the relationship between the number of turnovers and the number of points scored for players in a recent NBA season. The correlation for these data is r = 0.92.
Refer to Exercise 15. Does the fact that r = 0.92 suggest that an increase in turnovers will cause NBA players to score more points? Explain your reasoning.Exercise 15.Here is a scatterplot showing
Infants who cry easily may be more easily stimulated than others. This may be a sign of higher IQ. Child development researchers explored the relationship between the crying of infants 4 to 10 days
Is it possible to use temperature to predict wind speed? Here is a scatterplot showing the average temperature (in degrees Fahrenheit) and average wind speed (in miles per hour) for 365 consecutive
Manatees are large, gentle, slow-moving sea creatures found along the coast of Florida. Many manatees are injured or killed by boats. Here is a scatterplot showing the relationship between the number
How do the nutritional characteristics of food products differ from drink products at Starbucks? The scatterplot shown here enhances the scatterplot from Exercise 6 by plotting the food products with
Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate for 12 women
Athletes who participate in the shot put, discus throw, and hammer throw tend to have different physical characteristics than other track and field athletes. The scatterplot shown here enhances the
Refer to your graph from Exercise 4. Describe the relationship between distance from hole and percent of putts made for the sample of professional golfers.Exercise 4.How well do professional golfers
How does the fuel consumption of a car change as its speed increases? Here are data for a British Ford Escort. Speed is measured in kilometers per hour, and fuel consumption is measured in liters of
Refer to your graph from Exercise 3. Describe the relationship between body weight and backpack weight for this group of hikers.Exercise 3.Ninth-grade students at the Webb Schools go on a backpacking
The scatterplot shows the relationship between the amount of fat (in grams) and number of calories in products sold at Starbucks. Describe the relationship between fat and calories for these
The scatterplot shows the relationship between height (in inches) and weight (in pounds) for the members of the United States 2016 Olympic Track and Field team. Describe the relationship between
How well do professional golfers putt from various distances to the hole? The data show various distances to the hole (in feet) and the percent of putts made at each distance for a sample of
Ninth-grade students at the Webb Schools go on a backpacking trip each fall. Students are divided into hiking groups of size 8 by selecting names from a hat. Before leaving, students and their
Identify the explanatory variable and the response variable for the following relationships, if possible. Explain your reasoning.a. The height and arm span of a sample of 50 teenagersb. The yield of
Identify the explanatory variable and the response variable for the following relationships, if possible. Explain your reasoning.a. The weight gain of corals in aquariums where the water temperature
What is a better predictor of the number of wins for a baseball team, the number of runs scored by the team or the number of runs they allow the other team to score? What variables can we use to
Refer to Exercise 91.a. How do the ranges of the two distributions compare? Justify your answer.b. Explain why the standard deviation of the total family incomes in the New Jersey sample is so much
The parallel dotplots show the total family income of randomly chosen individuals from Indiana (38 individuals) and New Jersey (44 individuals). Means and standard deviations are given below the
The following Normal probability plot shows the distribution of points scored for the 551 players in a single NBA season.If the distribution of points was displayed in a histogram, what would be the
A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports
About what proportion of the cockroaches will have weights greater than 83 grams?a. 0.0228b. 0.0668c. 0.1587d. 0.9332e. 0.0772The weights of laboratory cockroaches can be modeled with a Normal
About what percent of the cockroaches have weights between 76 and 84 grams?a. 99.7%b. 95%c. 68%d. 47.5%e. 34%The weights of laboratory cockroaches can be modeled with a Normal distribution having
Point C on this Normal curve corresponds toa. 84 grams.b. 82 grams.c. 78 grams.d. 76 grams.e. 74 grams.The weights of laboratory cockroaches can be modeled with a Normal distribution having mean 80
Two measures of center are marked on the density curve shown. Which of the following is correct?a. The median is at the yellow line and the mean is at the red line.b. The median is at the red line
Refer to Exercise 76.a. Use your calculator to make a Normal probability plot of the data. Sketch this graph on your paper.b. What does the graph in part (a) imply about whether the distribution of
Refer to Exercise 75.a. Use your calculator to make a Normal probability plot of the data. Sketch this graph on your paper.b. What does the graph in part (a) imply about whether the distribution of
In 1798, the English scientist Henry Cavendish measured the density of the earth several times by careful work with a torsion balance. The variable recorded was the density of the earth as a multiple
The Normal probability plot displays data on the areas (in thousands of square miles) of each of the 50 states. Use the graph to determine if the distribution of land area is approximately Normal. -2
The following figure is a Normal probability plot of the heart rates of 200 male runners after 6 minutes of exercise on a treadmill. Use the graph to determine if this distribution of heart rates is
The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median
We collected data on the tuition charged by colleges and universities in Michigan. Here are some numerical summaries for the data:Based on the relationship between the mean, standard deviation,
Here are the lengths (in feet) of 44 great white sharks:A dotplot of the data and summary statistics are shown below. Is this distribution of shark length approximately Normal? Justify your answer
Consumer Reports magazine collected data on the usable capacity (in cubic feet) of a sample of 36 side-byside refrigerators. Here are the data:A histogram of the data and summary statistics are shown
The amount of time Ricardo spends brushing his teeth follows a Normal distribution with unknown mean and standard deviation. Ricardo spends less than 1 minute brushing his teeth about 40% of the
Refer to Exercise 21. Suppose that the corrected long-jump distances are converted from centimeters to meters (note that 100 cm =1 m ).a. What shape would the resulting distribution have? Explain
A used-car salesman has 28 cars in his inventory, with prices ranging from $11,500 to $25,000. For a Labor Day sale, he reduces the price of each car by $500. What effect will this reduction have on
The dotplot shows the EPA highway gas mileage estimates in miles per gallon (mpg) for a random sample of 21 model year 2018 midsize cars. Explain why this distribution of highway gas mileage is not
The histogram displays the percent of foreign-born residents in each of the 50 states.12 Explain why this distribution of the percent of foreign born residents in the states is not approximately
An airline flies the same route at the same time each day. The flight time varies according to a Normal distribution with unknown mean and standard deviation. On 15% of days, the flight takes more
The supplier is considering two changes to reduce to 1% the percentage of its large-cup lids that are too small. One strategy is to adjust the mean diameter of its lids. Another option is to alter
a. What percent of large lids are too small to fit?b. What percent of large lids are too big to fit?c. Compare your answers to parts (a) and (b). Does it make sense for the lid manufacturer to try to
A local post office weighs outgoing mail and finds that the weights of first-class letters are approximately Normally distributed with a mean of 0.69 ounce and a standard deviation of 0.16 ounce.a.
Scores on the Wechsler Adult Intelligence Scale (an IQ test) for the 20- to 34-year-old age group are approximately Normally distributed with μ = 110 and σ = 25 .a. What percent of people aged 20
The percent of the observations that are classified as outliers by the 1.5 × IQR rule is the same in any Normal distribution. What is this percent? Show your method clearly.
The deciles of any distribution are the values at the 10th, 20th, … , 90th percentiles. The first and last deciles are the 10th and the 90th percentiles, respectively. What are the first and last
Refer to Exercise 62. Find the 85th percentile of Djokovic’s first-serve speeds.Exercise 62.Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds can be
Refer to Exercise 61. Find the 20th percentile of Mrs. Starnes’s Sudoku times for easy puzzles.Exercise 61.Mrs. Starnes enjoys doing Sudoku puzzles. The time she takes to complete an easy puzzle
Professional tennis player Novak Djokovic hits the ball extremely hard. His first-serve speeds can be modeled by a Normal distribution with mean 112 miles per hour (mph) and standard deviation 5
Mrs. Starnes enjoys doing Sudoku puzzles. The time she takes to complete an easy puzzle can be modeled by a Normal distribution with mean 5.3 minutes and standard deviation 0.9 minute.a. What
Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.a. z < −2.46b. 0.89 < z < 2.46
Find the proportion of observations in a standard Normal distribution that satisfies each of the following statements.a. z > −1.66b. −1.66 < z < 2.85
Refer to Exercise 56. According to the same health information website, a diastolic blood pressure between 80 and 90 indicates borderline high blood pressure. About what percent of adults have
Refer to Exercise 55. About what percent of the meals ordered contained between 1200 mg and 1800 mg of sodium?Exercise 55.A study investigated about 3000 meals ordered from Chipotle restaurants using
According to a health information website, the distribution of adults’ diastolic blood pressure (in millimeters of mercury) can be modeled by a Normal distribution with mean 70 and standard
A study investigated about 3000 meals ordered from Chipotle restaurants using the online site Grubhub. Researchers calculated the sodium content (in milligrams) for each order based on Chipotle’s
Refer to Exercise 48. A player with a batting average below 0.200 is at risk of sitting on the bench during important games. About what percent of players are at risk?Exercise 48.In baseball, a
Refer to Exercise 47. About what percent of 9-ounce bags of this brand of potato chips weigh less than the advertised 9 ounces? Is this likely to pose a problem for the company that produces these
Refer to Exercise 48. Use the 68–95–99.7 rule to answer the following questions.a. About what percent of Major League Baseball players with 100 plate appearances had batting averages of 0.363 or
Refer to Exercise 47. Use the 68–95–99.7 rule to answer the following questions.a. About what percent of bags weigh less than 9.02 ounces? Show your method clearly.b. A bag that weighs 9.07
Estimate the mean and standard deviation of the Normal density curve below. 10 15 20 25 30 35 40 45 50
Estimate the mean and standard deviation of the Normal density curve below. 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
In baseball, a player’s batting average is the proportion of times the player gets a hit out of his total number of times at bat. The distribution of batting averages in a recent season for Major
The weights of 9-ounce bags of a particular brand of potato chips can be modeled by a Normal distribution with mean μ = 9.12 ounces and standard deviation σ = 0.05 ounce . Sketch the Normal density
The figure displays two density curves that model different distributions of quantitative data. Identify the location of the mean and median by letter for each graph. Justify your answers. (а) ABC
The figure displays two density curves that model different distributions of quantitative data. Identify the location of the mean and median by letter for each graph. Justify your answers. (а) (b)
Mr. Shrager does not always let his statistics class out on time. In fact, he seems to end class according to his own “internal clock.” The density curve models the distribution of the amount of
An Internet reaction time test asks subjects to click their mouse button as soon as a light flashes on the screen. The light is programmed to go on at a randomly selected time after the subject
How does your web browser get a file from the Internet? Your computer sends a request for the file to a web server, and the web server sends back a response. For one particular web server, the time
Where’s the bus? Sally takes the same bus to work every morning. The amount of time (in minutes) that she has to wait for the bus can be modeled by a uniform distribution on the interval from 0
Students were asked, “Are you right-handed, lefthanded, or ambidextrous?” The responses (R=right-handed, L = lefthanded, A = ambidextrous.a. Make an appropriate graph to display these data.b.
The dotplot displays data on students’ responses to the question “How long does it usually take you to travel to school?” Describe the distribution.We used Census At School’s Random Data
If the distribution of absences was displayed in a histogram, what would be the best description of the histogram’s shape?a. Symmetricb. Uniformc. Skewed leftd. Skewed righte. Cannot be
What is the interquartile range (IQR) for the distribution of absences?a. 1b. 2c. 3d. 5e. 14The number of absences during the fall semester was recorded for each student in a large elementary school.
George’s average bowling score is 180; he bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. Bill’s average bowling score is 190; he bowls in a league
Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 21 and standard deviation 5. Wayne’s standardized score on the ACT was −0.6. What was Wayne’s actual ACT
When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam’s distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean
Jorge’s score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score fallsa. Between the minimum and the first quartile.b. Between the first quartile
The scores on Ms. Martin’s statistics quiz had a mean of 12 and a standard deviation of 3. Ms. Martin wants to transform the scores to have a mean of 75 and a standard deviation of 12. What
In 2016, taxicabs in Los Angeles charged an initial fee of $2.85 plus $2.70 per mile. In equation form, Fare Fare = 2.85 + 2.7(miles). At the end of a month, a businessman collects all his taxicab
Clarence measures the diameter of each tennis ball in a bag with a standard ruler. Unfortunately, he uses the ruler incorrectly so that each of his measurements is 0.2 inch too large. Clarence’s
Coach Ferguson uses a thermometer to measure the temperature (in degrees Fahrenheit) at 20 different locations in the school swimming pool. An analysis of the data yields a mean of 77°F and a
Refer to Exercise 24. Suppose each car’s price is reduced by 10% instead of $500. What effect will this discount have on each of the following characteristics of the resulting price distribution?a.
Refer to Exercise 23. Suppose each teacher receives a 5% raise instead of a $1000 raise. What effect will this raise have on each of the following characteristics of the resulting salary
Refer to Exercise 22. Suppose that the distances from the tops of the students’ heads to the ground are converted from inches to feet (note that 12 in.=1 ft).a. What shape would the resulting
A school system employs teachers at salaries between $38,000 and $70,000. The teachers’ union and school board are negotiating the form of next year’s increase in the salary schedule. Suppose
A dotplot of the distribution of height for Mrs. Navard’s class is shown, along with some numerical summaries of the data.Suppose that Mrs. Navard has the entire class stand on a 6-inch-high

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