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All Textbook Solutions for Introduction To Probability And Statistics

Quantitative or Qualitative? Identify each variable as quantitative or qualitative: a. Ethnic origin of a candidate for public office b. Score (0100) on a placement examination c. Fast-food restaurant preferred by a student(McDonald’s, Burger King, or Carl’s Jr.) d. Mercury concentration in a sample of tuna Symmetric or Skewed? Do you expect the distributions of the following variables to be symmetric or skewed? Explain. a. Price of an 8-ounce can of peas b. Height in inches of freshman women at your university c. Number of broken taco shells in a package of 100 shells d. Number of ticks found on each of 50 trapped cottontail rabbits Continuous or Discrete? Identify each variable as continuous or discrete: a. Length of time between arrivals at a medical clinic b. Time required to finish an examination c. Weight of two dozen shrimp d. A person’s body temperature e. Number of people waiting for treatment at a hospitalemergency room Continuous or Discrete, again Identify each variable as continuous or discrete: a. Number of properties for sale by a real estate agency b. Depth of a snowfall c. Length of time for a driver to respond when about to have a collision d. Number of aircraft arriving at the Atlanta airport in a given hour World Lakes A lake is a body of water surrounded by land. Hence, some bodies of water named “seas,” like the Caspian Sea, are actually salt lakes. In the table that follows, the length in miles is listed for the major natural lakes of the world, excluding the Caspian Sea, which has a length of 760 miles.5 a. Use a stem and leaf plot to describe the lengths of the world’s major lakes. b. Use a histogram to display these same data. How does this compare to the stem and leaf plot in part a? c. Are these data symmetric or skewed? If skewed, what is the direction of the skewing?6RWYL Election Results The 2016 election was a race in which Donald Trump defeated Hillary Clinton and other candidates, winning 304 electoral votes, or 57% of the 538 available. However, Trump only won46.1% of the popular vote, while Clinton won 48.2%. The popular vote (in thousands) for Donald Trump in each of the 50 states is listed as follows18: a. By just looking at the table, what shape do you think the distribution for the popular vote by state will have? b. Draw a relative frequency histogram to describe the distribution of the popular vote for President Trump in the 50 states. c. Did the histogram in part b confirm your guess in part a? Are there any outliers? How can you explain them?8RWYL 9RWYL Pulse Rates A group of 50 biomedical students recorded their pulse rates by counting the numberof beats for 30 seconds and multiplying by 2. a. Why are all of the measurements even numbers? b. Draw a stem and leaf plot to describe the data, splittingeach stem into two lines. c. Construct a relative frequency histogram for the data. d. Write a short paragraph describing the distribution ofthe student pulse rates.11RWYL 12RWYL Gasoline Tax The following are the 2017 state gasoline tax in cents per gallon for the 50 U.S. states and the District of Columbia. a. Draw a stem and leaf display for the data. b. How would you describe the shape of this distribution? c. Are there states with unusually high or low gasoline taxes? If so, which states are they?14RWYL 15RWYL 16RWYL Kentucky Derby The following data set shows the winning times (in seconds) for the Kentucky Derby races from 1950 to 2017. a. Do you think there will be a trend in the winning times over the years? Draw a line chart to verify your answer. b. Use a graph to describe the distribution of winning times. Comment on the shape of the distribution and look for any unusual times.18RWYL Old Faithful The following data are the waiting times between eruptions of the Old Faithfulgeyser in Yellowstone National Park.25 Use a graph to describe the waiting times. If there are any unusual features in your graph, see if you can think of any practical explanation for them.20RWYL 1CS 2CS Experimental UnitsDefine the experimental units for the variables described in Exercises 15. 1. Gender of a student Experimental UnitsDefine the experimental units for the variables described in Exercises 15. 2. Number of errors on a midterm exam Experimental UnitsDefine the experimental units for the variables described in Exercises 15. 3. Age of a cancer patient Experimental UnitsDefine the experimental units for the variables described in Exercises 15. 4.Number of flowers on an azalea plant Experimental UnitsDefine the experimental units for the variables described in Exercises 15. 5. Color of a car entering a parking lot Qualitative or Quantitative? Are the variables in Exercises69 qualitative or quantitative? 6. Amount of time it takes to assemble a simple puzzle Qualitative or Quantitative? Are the variables in Exercises69 qualitative or quantitative? 7. Number of students in a first-grade classroom Qualitative or Quantitative? Are the variables in Exercises69 qualitative or quantitative? 8. Rating of a newly elected politician (excellent, good,fair, poor)Qualitative or Quantitative? Are the variables in Exercises69 qualitative or quantitative? 9. State in which a person lives Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 10. Population in a certain area of the United States Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 11. Weight of newspapers recycled on a single day Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 12. Number of claims filed with an insurance company during a single day Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 13. Number of consumers in a poll of 1,000 who consider nutritional labeling on food products to be important Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 14. Number of boating accidents along a 50-mile stretch of the Colorado River Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 15. Time required to complete a questionnaire Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 16. Cost of a head of lettuce Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 17. Number of brothers and sisters you have Discrete or Continuous? Are the variables in Exercises 1018 discrete or continuous? 18. Yield of wheat (in bushels) from a one-acre plot Populations or Samples? In Exercises 1922, determine whether the data collected represents a population or a sample. 19. A researcher uses a statewide database to determine the percentage of Michigan drivers who have had an accident in the last 5 years.Populations or Samples? In Exercises 1922, determine whether the data collected represents a population or a sample. 20. One thousand citizens were interviewed and their opinions regarding gun control were recorded.Populations or Samples? In Exercises 1922, determine whether the data collected represents a population or a sample. 21. Twenty animals are put on a new diet and their weight gain over 3 months is recorded.Populations or Samples? In Exercises 1922, determine whether the data collected represents a population or a sample. 22. The income distribution of the top 10% of wage earners in the United States is determined using data from the Internal Revenue Service.Parking on Campus Six vehicles selected from a campus vehicle database are shown in the table. a. What are the experimental units? b. List the variables that are being measured. What types are they? c. Is this univariate, bivariate, or multivariate data?Past U.S. Presidents A data set gives the ages at death for each of the 38 past presidents of the United States now deceased. a. Is this data set a population or a sample? b. What is the variable being measured? c. Is the variable in part b quantitative or qualitative?Voter Attitudes You are a candidate for your state legislature, and you want to survey voter attitudes about your chances of winning. a. What is the population that is of interest to you and from which you want to choose your sample? b. How is the population in part a dependent on time?Cancer Survival Times A researcher wants to estimate the survival time of a cancer patient after a course of radiation therapy. a. What is the variable of interest to the researcher? b. Is the variable in part a qualitative, quantitative discrete, or quantitative continuous? c. What is the population of interest? d. How could the researcher select a sample from the population? e. What problems might occur in sampling from this population?New Teaching Methods A researcher wants to know whether a new way of teaching reading to deaf students is working. She measures a student’s score on a reading test before and after being taught using the new method. a. What is the variable being measured? What type of variable is it? b. What is the experimental unit? c. What is the population of interest?Pie and Bar Charts The data in Exercises 13 represent different ways to classify a group of 100 students in a statistics class. Construct a bar chart and pie chart to describe each set of data.Pie and Bar Charts The data in Exercises 13 represent different ways to classify a group of 100 students in a statistics class. Construct a bar chart and pie chart to describe each set of data.Pie and Bar Charts The data in Exercises 13 represent different ways to classify a group of 100 students in a statistics class. Construct a bar chart and pie chart to describe each set of data.Groups of People Fifty people are grouped into four categories—A, B, C, and D—and the number of people who fall into each category is shown in the table: a. Construct a pie chart to describe the data. b. Construct a bar chart to describe the data. c. Does the shape of the bar chart in part b change depending on the order of presentation of the four categories? Is the order of presentation important? d. What proportion of the people are in category B, C, or D? e. What percentage of the people are not in category B?Presidential Popularity After the elections of 2016, apoll was taken to study the approval ratings for pastpresidents George W. Bush and Barack Obama. Thepoll, involving 1,009 U.S. adults 18 years or olderlivingin the United States and the District of Columbia,gives approval ratings by gender, race, age, andparty ID.1 Use this data for Exercises 610. Draw a bar chart to describe the approval rating ofGeorge W. Bush based on party ID.Presidential Popularity After the elections of 2016, a poll was taken to study the approval ratings for past presidents George W. Bush and Barack Obama. The poll, involving 1,009 U.S. adults 18 years or older living in the United States and the District of Columbia, gives approval ratings by gender, race, age, and party ID.1 Use this data for Exercises 610. 6. Draw a bar chart to describe the approval rating of George W. Bush based on party ID.Presidential Popularity After the elections of 2016, a poll was taken to study the approval ratings for past presidents George W. Bush and Barack Obama. The poll, involving 1,009 U.S. adults 18 years or older living in the United States and the District of Columbia, gives approval ratings by gender, race, age, and party ID.1 Use this data for Exercises 610. 7. Draw a bar chart to describe the approval rating of George W. Bush based on age.Presidential Popularity After the elections of 2016, a poll was taken to study the approval ratings for past presidents George W. Bush and Barack Obama. The poll, involving 1,009 U.S. adults 18 years or older living in the United States and the District of Columbia, gives approval ratings by gender, race, age, and party ID.1 Use this data for Exercises 610. 8. Draw a bar chart to describe the approval rating of Barack Obama based on party ID.Presidential Popularity After the elections of 2016, a poll was taken to study the approval ratings for past presidents George W. Bush and Barack Obama. The poll, involving 1,009 U.S. adults 18 years or older living in the United States and the District of Columbia, gives approval ratings by gender, race, age, and party ID.1 Use this data for Exercises 610. 9. Draw a bar chart to describe the approval rating of Barack Obama based on age.10E 11E 12E 13E 14E 15E Back to Work How long does it take you to adjust to your normal work routine after coming back from vacation? A bar graph with data from a USA Today snapshot is shown here: a. Are all of the opinions accounted for in the table? Add another category if necessary. b. Is the bar chart drawn accurately? That is, are the three bars in the correct proportion to each other? c. Use a pie chart to describe the opinions. Which graph is more interesting to look at?17E 18E 19E 20E 21E DotplotsConstruct a dotplot for the data given in Exercises 12. Describe the shape of the distributionand look for any outliers. 1. 2.0, 1.0, 1.1, 0.9, 1.0, 1.2, 1.3, 1.1, 0.9, 1.0, 0.9, 1.4, 0.9, 1.0, 1.0 DotplotsConstruct a dotplot for the data given in Exercises 12. Describe the shape of the distributionand look for any outliers. 2. 53, 61, 58, 56, 58, 60, 54, 54, 62, 58, 60, 58, 56, 56, 58 Stem and Leaf I Construct a stem and leaf plot for these 50 measurements and answer the questions in Exercises 35. 3. Describe the shape of the distribution. Do you see any outliers?Stem and Leaf I Construct a stem and leaf plot for these 50 measurements and answer the questions in Exercises 35. 4. Use the stem and leaf plot to find the smallest observation.Stem and Leaf I Construct a stem and leaf plot for these 50 measurements and answer the questions in Exercises 35. 5. Find the eighth and ninth largest observations.Stem and Leaf II Use the following set of data toanswer the questions in Exercises 68. 6. Draw a stem and leaf plot, using the number in the ones place as the stem.Stem and Leaf II Use the following set of data toanswer the questions in Exercises 68. 7. Draw a stem and leaf plot, using each number in the ones place twice to form the stems.8E 9E Comparing Graphs A discrete variable can take on only the values 0, 1, or 2. Use the set of 20 measurements on this variable to answer the questions in Exercises 912. 10. How could you define the stem and leaf for this data set? Draw the stem and leaf plot.11E 12E 13E 14E 15E 16E 17E Calcium Contents The calcium content (Ca)of a powdered mineral substance was analyzed10 times with the following percent compositionrecorded. a. Draw a dotplot to describe the data. (HINT: Thescale of the horizontal axis should range from 2.60to 2.90.) b. Draw a stem and leaf plot for the data. Use the numbersin the hundredths and thousandths place as thestem. c. Are any of the measurements inconsistent with theother measurements, indicating that the technicianmay have made an error in the analysis?19E 20E 21E 22E 23E 24E American Presidents The following table lists the ages at the time of death for the 38 deceased American presidents from George Washington to Ronald Reagan5: a. Before you graph the data, think about the distribution of the ages at death for the presidents. What shape do you think it will have? b. Draw a stem and leaf plot for the data. Describe the shape. Does it surprise you? c. The five youngest presidents at the time of death appear in the lower “tail” of the distribution. Identify these five presidents. d. Three of the five youngest have one thing in common. What is it?Graphing Relative Frequency Histograms Construct a relative frequency histogram using the statistical tables in Exercises 12. How would you describe the shape of the distribution?Graphing Relative Frequency Histograms Construct a relative frequency histogram using the statistical tables in Exercises 12. How would you describe the shape of the distribution?Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 3. 33 or more Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 4. 32 to < 33.5 Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 5. less than 31 Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 6. Greater than or equal to 33.5 Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 7. at least 34 Interpreting Relative Frequency Histograms Use the relative frequency histogram that follows to calculate the proportion of measurements falling into the intervals given in Exercises 38. Remember that the classes include the left boundary point, but not the right. 8. At least 31.5 but less than 33.5 Class Boundaries In Exercises 912, use the information given to find a convenient class width. Then list theclass boundaries that can be used to create a relative frequency histogram. 9. classes for n = 50 measurements; minimum value = 10; maximum value = 110 Class Boundaries In Exercises 912, use the information given to find a convenient class width. Then list theclass boundaries that can be used to create a relative frequency histogram. 10. 6 classes for n = 20 measurements; minimum value = 25.5; maximum value = 76.8 11E 12E 13E 14E Relative Frequency Histogram I Construct a relative frequency histogram for these50 measurements using classes starting at 1.6 with a class width of .5. Then answer the questions in Exercises 1316. 15. What is the probability that a measurement drawn at random from this set will be greater than or equal to 3.6?16E 17E 18E 19E 20E 21E 22E 23E 24E A Recurring Illness The length of time (in months) between the onset of a particular illness and its recurrence was recorded for n= 50 patients: a. Construct a relative frequency histogram for the data. b. Would you describe the shape as roughly symmetric, skewed right, or skewed left? c. Find the fraction of recurrence times less than or equal to 10 months.26E 27E 28E 29E 30E 31E Student Heights The self-reported heights of 105 students in a biostatistics class are described in the relative frequency histogram shown here. a. Describe the shape of the distribution. b. Do you see any unusual feature in this histogram? c. Can you think of an explanation for the two peaks in the histogram? Is there something that is causing the heights to mound up in two separate peaks? What is it?33E Raisins The number of raisins in each of 14miniboxes (1/2 -ounce size) was counted for ageneric brand and for Sunmaid brand raisins. Thetwo data sets are shown here: a. What are the mean and the standard deviation for thegeneric brand? b. What are the mean and the standard deviation for theSunmaid brand? c. Compare the centers and variabilities of the twobrands using the results of parts a and b.Raisins, continued Refer to Exercise 1. a. Find the median, the upper and lower quartiles, andthe IQR for each of the two data sets. b. Construct two box plots on the same horizontal scaleto compare the two sets of data. c. Draw two stem and leaf plots and describe theshapes of the two data sets. Do the box plots inpart b verify these results? d. If none of the boxes of raisins are being underfilled(that is, they all weigh approximately 1/2 ounce),what do your results say about the average numberof raisins for the two brands?3RWYL 4RWYL 5RWYL 6RWYL 7RWYL 8RWYL 9RWYL 10RWYL 11RWYL 12RWYL 13RWYL 14RWYL 15RWYL 16RWYL 17RWYL 18RWYL 19RWYL 20RWYL 21RWYL 22RWYL 23RWYL 24RWYL 25RWYL Measures of CenterFor the data sets in Exercises 14, calculate the mean, the median, and the mode. Locate these measures on a dotplot. 1.n=5measurements:0,5,1,1,3 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E Fortune 500 Revenues Ten of the 50largestbusinesses in the United States, randomlyselected from the Fortune 500, are listedas follows along with their revenues (in millions of dollars)4: a. Draw a stem and leaf plot for the data. Are the dataskewed? b. Calculate the mean revenue for these 10 businesses.Calculate the median revenue. c. Which of the two measures in part b best describesthe center of the data? Explain.19E 20E 21E 22E Calculating the Standard Deviation I For the data setsin Exercises 13, calculate the sample variance, s2,using (1) the definition formula and (2) the computingformula. Then calculate the sample standard deviation, s. 1. n=5measurements:2,1,1,3,5 Calculating the Standard Deviation I For the data sets in Exercises 13, calculate the sample variance, s2, using (1) the definition formula and (2) the computing formula. Then calculate the sample standard deviation, s. 2. n=8measurements:4,1,3,1,3,1,2,2 Calculating the Standard Deviation I For the data sets in Exercises 13, calculate the sample variance, s2, using (1) the definition formula and (2) the computing formula. Then calculate the sample standard deviation, s. 3. n=8measurements:3,1,5,6,4,4,3,5 4E 5E 6E 7E 8E For the data sets in Exercises 79, find the range, the sample variance and the sample standard deviation. 9. Time on Task In a psychology experiment, 10 subjectswere given 5 minutes to complete a task. Their time ontask (in seconds) is recorded. 175 190 250 230 240 200 185 190 225 265 10E 11E Sleep and the College Student A group of 10 collegestudents were asked to report how many hours that theyslept on the previous night with the following results: 7 6 7.25 7 8.5 5 8 7 6.75 6 a. Find the mean and the standard deviation of the numberof hours of sleep for these 10 students. b. What is the most frequently reported measurement?What is the name for this measure of center?Gas Mileage The miles per gallon (mpg) foreach of 20 medium-sized cars selected from a productionline during the month of March follow. a. What are the maximum and minimum miles per gallon?What is the range? b. Construct a relative frequency histogram for thesedata. How would you describe the shape of thedistribution? c. Find the mean and the standard deviation.Polluted Seawater Petroleum pollution in seas andoceans stimulates the growth of some types of bacteria.Acount of the number of bacteria (per 100 milliliters) in 10portions of seawater gave these readings: 49, 70, 54, 67, 59, 40, 61, 69, 71, 52 a. Calculate the range. b. Calculate x and s. c. The range is about how many standard deviations?15E Approximating the Standard Deviation For the data setsin Exercises 13, use the range to approximate the valueof s. Then calculate the actual value of s. Is the actualvalue close to the estimate? 1. n=10measurements:5,2,3,6,1,2,4,5,1,3 Approximating the Standard Deviation For the data sets in Exercises 13, use the range to approximate the value of s. Then calculate the actual value of s. Is the actual value close to the estimate? 2. n=10measurements:25,26,26,26,26,28,2726,25,28,24,28,27,2525,28,25,28,29,24,2824,24,28,30,24,22,27 3E 4E 5E Data Set I A distribution of measurements is relativelymound-shaped with a mean of 50 and a standard deviationof 10. Use this information to find the proportion ofmeasurements in the intervals given in Exercises 611. 6. Between 40 and 60 7E Data Set I A distribution of measurements is relatively mound-shaped with a mean of 50 and a standard deviation of 10. Use this information to find the proportion of measurements in the intervals given in Exercises 611. 8. Between 30 and 60 9E 10E 11E 12E Data Set II A distribution of measurements has a mean of 75 and a standard deviation of 5. You know nothing else about the size or shape of the data. Use this information to find the proportion of measurements in the intervals given in Exercises 1214. 13. Between 65 and 85 14E 15E 16E 17E 18E 19E Breathing Rates Breathing rates for humans canbe as low as 4 breaths per minute or as high as 70 or75 for a person doing strenuous exercise. Suppose thatthe resting breathing rates for college-age students havea distribution that is mound-shaped, with a mean of12 and a standard deviation of 2.3 breaths per minute.What fraction of all students have breathing rates in thefollowing intervals? a. 9.7 to 14.3 breaths per minute b. 7.4 to 16.6 breaths per minute c. More than 18.9 or less than 5.1 breaths per minute 21E 22E 23E 24E 25E 26E 27E 28E 29E 30E 31E TV Commercials The mean duration of televisioncommercials on a given network is 75 seconds, with astandard deviation of 20 seconds. Assume that durationsare approximately normally distributed. a. What is the approximate probability that a commercialwill last less than 35 seconds? b. What is the approximate probability that a commercialwill last longer than 55 seconds?z-ScoresFor the data sets in Exercises 13, find the mean,the standard deviation, and the z-scores correspondingto the minimum and maximum in the data set. Do thez-scores indicate that there are possible outliers in thesedata sets? 1. n=12measurements:8,7,1,4,6,6,4,5,7,6,3,0 z-ScoresFor the data sets in Exercises 13, find the mean, the standard deviation, and the z-scores corresponding to the minimum and maximum in the data set. Do the z-scores indicate that there are possible outliers in these data sets? 2. n=11measurements:2.3,1.0,2.1,6.5,2.8,7.8,1.7,2.9,4.4,5.1,2.0 z-ScoresFor the data sets in Exercises 13, find the mean, the standard deviation, and the z-scores corresponding to the minimum and maximum in the data set. Do the z-scores indicate that there are possible outliers in these data sets? 3. n=13measurements:3,9,10,2,6,7,5,8,6,6,4,9,25 Median and Quartiles For the data in Exercises 46, calculate the median and the upper and lower quartiles. 4. n=7measurements:6,7,3,2,8,10,4 Median and Quartiles For the data in Exercises 46, calculate the median and the upper and lower quartiles. 5. n=7measurements:5,6,0,2,5,1,7,6,3 Median and Quartiles For the data in Exercises 46, calculate the median and the upper and lower quartiles. 6. n=6measurements:1,7,4,5,2,9 -Number Summary and the Box Plot For each of the data sets in Exercises 79, calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers. 7. n=15measurements:19,12,16,0,14,9,6,1,12,13,10,19,7,5,8 Five-Number Summary and the Box Plot For each of the data sets in Exercises 79, calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers. 8. n=8measurements:.23,.30,.35,.41,.56,.58,.76,.80 Five-Number Summary and the Box Plot For each of the data sets in Exercises 79, calculate the five-number summary and the interquartile range. Use this information to construct a box plot and identify any outliers 9. n=11measurements:25,22,26,23,27,2628,18,25,24,12 10E z-Scores vs. Box Plots For the data sets in Exercises 10 and 11, find the mean, the standard deviation and the five-number summary. Find the z-scores for the minimum and maximum observations. Then construct a box plot and identify any outliers. Are the results using z-scores the same as those based on the box plots? 11. n=13measurements:3,9,10,2,6,7,5,8,6,6,4,9,25(seeExercise3)Percentiles What are the percentiles in Exercises 1215and what do they mean in practical terms? 12. You scored 78 which was the 69th percentile on aplacement test.Percentiles What are the percentiles in Exercises 1215 and what do they mean in practical terms? 13. In the U.S. population, about 14.5% of all men aresix feet tall or taller.Percentiles What are the percentiles in Exercises 1215 and what do they mean in practical terms? 14. A score of 513 on the MCAT (Medical CollegeAdmissions Test) is the 90th percentile.Percentiles What are the percentiles in Exercises 1215 and what do they mean in practical terms? 15. Forty-six percent of all 19-year-old females in acertain height-weight category have a BMI (body massindex) greater than 21.9.For the data in Exercises 1617, find the sample meanand the sample standard deviation and calculate thez-scores for the largest and smallest observations. Arethere any unusually large or small observations? 16. TV Viewers A sample of 25 households ina particular area gave the following estimates ofthe number of television viewing hours in primetime per household per week:For the data in Exercises 1617, find the sample meanand the sample standard deviation and calculate thez-scores for the largest and smallest observations. Arethere any unusually large or small observations? 17. Packaging Hamburger Meat The weights(in pounds) of 27 packages of ground beef arelisted here in order from smallest to largest.€For the data in Exercises 1819, find the five-number summary and the IQR. Use this information to construct a box plot and identify any outliers. 18. Tuna Fish, again The prices of a 6-ounce can or a 7.06-ounce pouch for 14 different brands of waterpacked light tuna, based on prices paid nationally in supermarkets, are shown herr1: .99 1.92 1.23 .85 .65 .53 1.41 1.12 .63 .67 .69 .60 .60 .66 For the data in Exercises 1819, find the five-number summary and the IQR. Use this information to construct a box plot and identify any outliers. 19. Polluted Seawater A count of the number of bacteria(per 100 milliliters) in 10 samples of seawater gavethese readings: 49, 70, 54, 67, 59, 40, 61, 69, 71, 52 20E 21E Presidential Vetoes The number of vetoesused by each of the 44 presidents is listed here,along with a box plot generated by MINITAB.6Usethe box plot to describe the shape of the distributionand identify any outliers.23E 24E Ages of Pennies Here are the ages of50 pennies, calculated as AGE =CURRENTYEAR =YEAR ON PENNY. The data havebeen sorted from smallest to largest. a. What is the average age of the pennies? b. What is the median age of the pennies? c. Based on the results of parts a and b, how wouldyou describe the age distribution of these 50pennies? d. Draw a box plot for the data set. Are there any outliers?Does the box plot confirm your description ofthe distribution’s shape?26E 1RWYL 2RWYL 3RWYL 4RWYL 5RWYL 6RWYL 7RWYL 8RWYL 9RWYL 10RWYL 11RWYL 12RWYL Armspan and Height Leonardo da Vinci(14521519) drew a sketch of a man, indicatingthat a person’s armspan (measuring across theback with arms outstretched to make a “T”) is roughlyequal to the person’s height. To test this claim, we measuredeight people with the following results: a. Draw a scatterplot for armspan and height. Use thesame scale on both the horizontal and vertical axes.Describe the relationship between the two variables. b. Calculate the correlation coefficient relating armspanand height. c. If you were to calculate the regression line for predictingheight based on a person’s armspan, howwould you estimate the slope of this line? d. Find the regression line relating armspan to a person’sheight. e. If a person has an armspan of 62 inches, what wouldyou predict the person’s height to be?14RWYL 15RWYL 16RWYL Movie Money Does the amount of moneya movie makes on a single weekend in any waypredict the movie’s success or failure? Or is amovie’s monetary success more dependent on the numberof weeks the movie remains in movie theaters? Thefollowing data was collected for the top 16 movies intheaters during a recent weekend.18 Use the tools that you have developed in this chapterto explore possible relationships between pairs ofvariables in the table. Which scatterplots might behelpful in your investigation? Which pairs of variableswill have a positive correlation? A negativecorrelation?18RWYL 19RWYL 20RWYL 1CS 2CS 3CS Side-by-Side Bar Charts Use side-by-side bar charts to describe the data in Exercises 12. 1. Twenty measurements on two categories—(A or B) and (X or Y): (A, X), (B, Y), (A, X), (A, Y), (B, X) (B, Y), (A, X), (B, Y), (A, X), (A, Y) (B, X), (B, X), (B, Y), (A, X), (B, X) (B, Y), (B, Y), (A, Y), (B, Y), (B, Y)Side-by-Side Bar Charts Use side-by-side bar charts to describe the data in Exercises 12. 2. n=242 measurements on two categories—(A, B, orC) and (1, 2, or 3)3E 4E Stacked Bar Charts Use stacked bar charts to describethe data sets in Exercises 34 (reproduced asExercises 56). Do the side-by-side pie charts or thestacked bar charts provide a better picture of the data 6E 7E 8E Consumer SpendingThe following table shows theaverage amounts spent per week by men and women ineach of four spending categories: a. What possible graphs could you use to compare thespending patterns of women and men? b. Choose two different graphs and use them to displaythe data. c. What can you say about the similarities or differencesin the spending patterns for men andwomen? d. Which of the two graphs used in part b provides abetter picture of the data?10E M&M’S The color distributions for two snack-sizebags of M&M’S® candies, one plain and one peanut,are shown in the table. Choose an appropriate graph andcompare the distributions.12E 13E 14E 15E 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E

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