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Mathematical Interest Theory 3rd Edition Leslie Jane, James Daniel, Federer Vaaler - Solutions

Using the data from Exercise 7 "Car Weight and Fuel Consumption," the P-value is 0.000.Data from Exercise 7Write a statement that interprets the P-value and includes a conclusion about linear correlation.
Using the data from Exercise 8 "Heights of Fathers and Sons," the P-value is 0.963.Data From Exercise 8Write a statement that interprets the P-value and includes a conclusion about linear correlation.
The table lists brain volumes (cm3) and IQ scores of five males (from Data Set 8 "IQ and Brain Size" in Appendix B).Data Set 8 Use the sample data to construct a scatterplot. Use the first variable for the x-axis. Based on the scatterplot, what do you conclude about a linear correlation?
The table lists chest sizes (distance around chest in inches) and weights (pounds) of anesthetized bears that were measured (from Data Set 9 "Bear Measurements" in Appendix B).Data Set 9Use the sample data to construct a scatter plot. Use the first variable for the x-axis. Based on the scatter
The table lists weights (pounds) and highway fuel consumption amounts (mpg) for a Hyundai Elantra, Nissan Altima, VW Passat, Buick Lucerne, Mercury Grand Marquis, Honda Civic, and Honda Accord.Use the sample data to construct a scatter plot. Use the first variable for the x-axis. Based on the
The table lists heights (in.) of fathers and the heights (in.) of their first sons (from Francis Galton).Use the sample data to construct a scatter plot. Use the first variable for the x-axis. Based on the scatter plot, what do you conclude about a linear correlation?
Using the data from Exercise 5 "Brain Volume and IQ," the linear correlation coefficient is r = 0.127.Data From Exercise 5Use Table 2-11 on page 71 to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a
Construct a frequency distribution of the 20 body temperatures (oF) listed below. (These data are from Data Set 3 "Body Temperatures" in Appendix B.) Use a class width of 0.5oF and a starting value of 97.0oF.
Construct a dotplot of the body temperatures listed in Exercise 1. Which does a better job of illustrating the distribution of the data: the histogram from Exercise 2 or the dotplot?Data from Ex.1
Listed below are the temperatures from nine males measured at 8 AM and again at 12 AM (from Data Set 3 "Body Temperatures" in Appendix B). Construct a scatter plot. Based on the graph, does there appear to be a relationship between 8 AM temperatures and 12 AM temperatures?
In a Marist survey of adults, these are the words or phrases that subjects find most annoying in conversation (along with their frequencies of response): like (127); just sayin' (81); you know (104); whatever (219); obviously (35). Construct a pie chart. Identify one disadvantage of a pie chart.
Use the same data from Exercise 7 to construct a Pareto chart. Which graph does a better job of illustrating the data: Pareto chart or pie chart? Data From Exe. 7. In a Marist survey of adults, these are the words or phrases that subjects find most annoying in conversation (along with their
Construct a frequency distribution. Use a class width of 5 hours and use a starting time of 235 hours.Refer to the data below, which are total home game playing times (hours) for all Major League Baseball teams in a recent year (based on data from Baseball Prospectus).
Construct the histogram corresponding to the frequency distribution from Exercise 1. For the values on the horizontal axis, use the class midpoint values. Which of the following comes closest to describing the distribution: uniform, normal, skewed left, skewed right?Refer to the data below, which
Refer to the data below, which are total home game playing times (hours) for all Major League Baseball teams in a recent year (based on data from Baseball Prospectus).a. The listed playing times are all rounded to the nearest whole number. Before rounding, are the exact playing times discrete data
The defunct website IncomeTaxList.com listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
Listed below are selling prices (dollars) of TVs that are 60 inches or larger and rated as a "best buy" by Consumer Reports magazine. Are the resulting statistics representative of the population of all TVs that are 60 inches and larger? If you decide to buy one of these TVs, what statistic is most
Listed below are the measured radiation absorption rates (in W>kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications
Listed below are measured amounts of caffeine (mg per 12 oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . . , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans? 0 0 34 34 34 45 41 51 55 36
Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of center? 20 18 23 30
Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women? 10.4 9.3 9.1 9.3 10.0 9.4 8.6 9.8 9.9 9.1 9.1 Find the (a) mean, (b) median, (c) mode, (d)
Listed below are the annual costs (dollars) of tuition and fees at the 10 most expensive colleges in the United States for a recent year (based on data from U.S. News & World Report). The colleges listed in order are Columbia, Vassar, Trinity, George Washington, Carnegie Mellon, Wesleyan, Tulane,
Listed below in dollars are the amounts it costs for marriage proposal packages at the different Major League Baseball stadiums. Five of the teams don't allow proposals. Are there any outliers?Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.
Listed below are annual U.S. sales of vinyl record albums (millions of units). The numbers of albums sold are listed in chronological order, and the last entry represents the most recent year. Do the measures of center give us any information about a changing trend over time?Find the (a) mean, (b)
In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?Find
USA Today published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S. drivers? Why or why not?
In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Can the results be used to describe the attractiveness of the
A sample of blood pressure measurements is taken from Data Set 1 "Body Data" in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have systolic and diastolic measurements. (Systolic is a measure of the force of blood being pushed through
Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 "Body Data"in Appendix B). Does there appear to be a difference?Find the mean and median for each of the two samples, then compare the two sets of results.
Waiting times (in seconds) of customers at the Madison Savings Bank are recorded with two configurations: single customer line; individual customer lines. Carefully examine the data to determine whether there is a difference between the two data sets that is not apparent from a comparison of the
Use the magnitudes (Richter scale) of the 600 earthquakes listed in Data Set 21 "Earthquakes" in Appendix B. In 1989, the San Francisco Bay Area was struck with an earthquake that measured 7.0 on the Richter scale. That earthquake occurred during the warm up period for the third game of the
Use the birth weights (grams) of the 400 babies listed in Data Set 4 "Births" in Appendix B. Examine the list of birth weights to make an observation about those numbers. How does that observation affect the way that the results should be rounded?Data Set4Refer to the indicated data set in Appendix
Find the mean of the data summarized in the frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as follows: (Exercise 29) 36.2 years; (Exercise 30) 44.1 years; (Exercise 31) 224.3; (Exercise 32) 255.1. Age (yr)
A student of the author earned grades of A, C, B, A, and D. Those courses had these corresponding numbers of credit hours: 3, 3, 3, 4, and 1. The grading system assigns quality points to letter grades as follows: A = 4; B = 3; C = 2; D = 1; F = 0. Compute the grade-point average (GPA) and round the
A student of the author earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned grades of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60% of the final grade, the final exam counts for 10%,
Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the
Here are four of the Verizon data speeds (Mbps) from Figure 3-1: 13.5, 10.2, 21.1, 15.1. Find the mean and median of these four values. Then find the mean and median after including a fifth value of 142, which is an outlier. (One of the Verizon data speeds is 14.2 Mbps, but 142 is used here as an
The quadratic mean (or root mean square, or R.M.S.) is used in physical applications, such as power distribution systems. The quadratic mean of a set of values is obtained by squaring each value, adding those squares, dividing the sum by the number of values n, and then taking the square root of
Listed below are the jersey numbers of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. What do the results tell us? 89 91 55 7 20 99 25 81 19 82 60 Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.
Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the results likely to be representative of all National Football League (NFL) players? 189 254 235 225
Listed below are the highest amounts of net worth (in millions of dollars) of celebrities. The celebrities are Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. What do the results tell us about the
Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard (the "Strip"). If you decide to stay at one of these hotels, what statistic is most relevant, other than the measures of center? Apart from price, identify one other important factor that would
Listed below are the numbers of Atlantic hurricanes that occurred in each year. The data are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of center? 8 9 8 7 9 15 5 6 8 4 12 7 8 2 Find the (a) mean, (b) median, (c)
Listed below are selling prices in dollars of TVs that are 60 inches or larger and rated as a "best buy" by Consumer Reports magazine. Are the measures of variation likely to be typical for all TVs that are 60 inches or larger? 1800 1500 1200 1500 1400 1600 1500 950 1600 1150 1500 1750 Find the
Listed below are the measured radiation absorption rates (in W>kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications
Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . . , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans? 0 0 34 34 34 45 41 51 55 36
Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation? 20 18 23
Listed below are foot lengths in inches of randomly selected Army women measured in the 1988 Anthropometric Survey (ANSUR). Are the statistics representative of the current population of all Army women? 10.4 9.3 9.1 9.3 10.0 9.4 8.6 9.8 9.9 9.1 9.1 Find the range, variance, and standard deviation
Listed below in dollars are the annual costs of tuition and fees at the 10 most expensive colleges in the United States for a recent year (based on data from U.S. News & World Report). The colleges listed in order are Columbia, Vassar, Trinity, George Washington, Carnegie Mellon, Wesleyan, Tulane,
Listed below are the amounts (dollars) it costs for marriage proposal packages at the different Major League Baseball stadiums. Five of the teams don't allow proposals. Are there any outliers, and are they likely to have much of an effect on the measures of variation?Find the range, variance, and
Listed below are annual U.S. sales of vinyl record albums (millions of units). The numbers of albums sold are listed in chronological order, and the last entry represents the most recent year. Do the measures of variation give us any information about a changing trend over time? 0.3 0.6 0.8 1.1 1.1
In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?Find
The 20 brain volumes (cm3) from Data Set 8 "IQ and Brain Size" in Appendix B have a mean of 1126.0 cm3 and a standard deviation of 124.9 cm3. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a brain volume of
In a study of speed dating conducted at Columbia University, female subjects were asked to rate the attractiveness of their male dates, and a sample of the results is listed below (1 = not attractive; 10 = extremely attractive). Can the results be used to describe the variation among attractiveness
A sample of blood pressure measurements is taken from Data Set 1 "Body Data" in Appendix B, and those values (mm Hg) are listed below. The values are matched so that 10 subjects each have a systolic and diastolic measurement.Find the coefficient of variation for each of the two samples; then
Listed below are pulse rates (beats per minute) from samples of adult males and females (from Data Set 1 "Body Data" in Appendix B). Does there appear to be a difference?Find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section
Waiting times (in seconds) of customers at the Madison Savings Bank are recorded with two configurations: single customer line; individual customer lines.Find the coefficient of variation for each of the two samples; then compare the variation. (The same data were used in Section 3-1.)
Use the magnitudes (Richter scale) of the 600 earthquakes listed in Data Set 21 "Earthquakes" in Appendix B. In 1989, the San Francisco Bay Area was struck with an earthquake that measured 7.0 on the Richter scale. If we add that value of 7.0 to those listed in the data set, do the measures of
Use the birth weights (grams) of the 400 babies listed in Data Set 4 "Births" in Appendix B. Examine the list of birth weights to make an observation about those numbers. How does that observation affect the way that the results should be rounded?Refer to the indicated data set in Appendix B. Use
Based on Data Set 1 "Body Data" in Appendix B, females have pulse rates with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. Is a pulse rate of 44 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.) Use the
Based on Data Set 1 "Body Data" in Appendix B, males have pulse rates with a mean of 69.6 beats per minute and a standard deviation of 11.3 beats per minute. Is a pulse rate of 50 beats per minute significantly low or significantly high? (All of these pulse rates are measured at rest.)
Based on Data Set 2 "Foot and Height" in Appendix B, adult males have foot lengths with a mean of 27.32 cm and a standard deviation of 1.29 cm. Is the adult male foot length of 30 cm significantly low or significantly high? Explain. Use the range rule of thumb to identify the limits separating
Based on Data Set 3 “Body Temperatures” in Appendix B, body temperatures of adults have a mean of 98.20°F and a standard deviation of 0.62°F. (The data from 12 AM on day 2 are used.) Is an adult body temperature of 100°F significantly low or significantly high?Use the range rule of thumb to
Refer to the frequency distribution in the given exercise and find the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these
Based on Data Set 1 "Body Data" in Appendix B, blood platelet counts of women have a bell-shaped distribution with a mean of 255.1 and a standard deviation of 65.4. (All units are 1000 cells>μL.) Using the empirical rule, what is the approximate percentage of women with platelet counts a. within 2
Based on Data Set 3 "Body Temperatures" in Appendix B, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°F and a standard deviation of 0.62°F. Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures a. within 1
Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced
Use the same population of {9 cigarettes, 10 cigarettes, 20 cigarettes} from Exercise 45. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does
Listed below are the jersey numbers of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII. What do the results tell us? 89 91 55 7 20 99 25 81 19 82 60 Find the range, variance, and standard deviation for the given sample data. Include appropriate
Listed below are the weights in pounds of 11 players randomly selected from the roster of the Seattle Seahawks when they won Super Bowl XLVIII (the same players from the preceding exercise). Are the measures of variation likely to be typical of all NFL players? 189 254 235 225 190 305 195 202 190
Listed below are the highest amounts of net worth (in millions of dollars) of celebrities. The celebrities are Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Are the measures of variation typical for
Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard (the "Strip"). How useful are the measures of variation for someone searching for a room? 212 77 121 104 153 264 195 244 Find the range, variance, and standard deviation for the given sample data.
Listed below are the numbers of Atlantic hurricanes that occurred in each year. The data are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation? 8 9 8 7 9 15 5 6 8 4 12 7 8 2 Find the range, variance, and
Data Set 29 "Coin Weights" lists weights (grams) of quarters manufactured after 1964. Those weights have a mean of 5.63930 g and a standard deviation of 0.06194 g. Identify the weights that are significantly low or significantly high. Consider a value to be significantly low if its z score is less
The tallest living man at the time of this writing is Sultan Kosen, who has a height of 251 cm. The shortest living man is Chandra Bahadur Dangi, who has a height of 54.6 cm. Heights of men have a mean of 174.12 cm and a standard deviation of 7.10 cm. Which of these two men has the height that is
Based on Data Set 1 "Body Data" in Appendix B, males have red blood cell counts with a mean of 4.719 and a standard deviation of 0.490, while females have red blood cell counts with a mean of 4.349 and a standard deviation of 0.402. Who has the higher count relative to the sample from which it
Based on Data Set 4 "Births" in Appendix B, newborn males have weights with a mean of 3272.8 g and a standard deviation of 660.2 g. Newborn females have weights with a mean of 3037.1 g and a standard deviation of 706.3 g. Who has the weight that is more extreme relative to the group from which they
The boxplot shown below results from the heights (cm) of males listed in Data Set 1 "Body Data" in Appendix B. What do the numbers in that boxplot tell us?Data Set1
Listed below are the measured radiation absorption rates (in W/ kg) corresponding to these cell phones: iPhone 5S, BlackBerry Z30, Sanyo Vero, Optimus V, Droid Razr, Nokia N97, Samsung Vibrant, Sony Z750a, Kyocera Kona, LG G2, and Virgin Mobile Supreme. The data are from the Federal Communications
Listed below are amounts of strontium-90 (in millibecquerels, or mBq) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from "An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s," by Mangano et. al., Science of the Total
Fourteen different second-year medical students at Bellevue Hospital measured the blood pressure of the same person. The systolic readings (mm Hg) are listed below. 138 130 135 140 120 125 120 130 130 144 143 140 130 150 Use the given data to construct a boxplot and identify the 5-number summary.
Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 "Body Data" in Appendix B.Use the given data sets in Appendix B. Use the boxplots to compare the two data sets.Data Set 1
Use the same scale to construct boxplots for the ages of the best actresses and best actors from Data Set 14 "Oscar Winner Age" in Appendix B. Use the given data sets in Appendix B. Use the boxplots to compare the two data sets. Data Set 14 ACTRESSES ACTORS 22 ......................44 37
Use the body mass indexes (BMIs) for males and females listed in Data Set 1 "Body Data."Use the given data sets in Appendix B. Use the boxplots to compare the two data sets.Data Set 1
Use the same scale to construct boxplots for the full IQ scores (IQF) for the low lead level group (group 1) and the high lead level group (group 3) in Data Set 7 "IQ and Lead" in Appendix B.Use the given data sets in Appendix B. Use the boxplots to compare the two data sets.Data Set 7
Repeat Exercise 33 "Pulse Rates" using modified boxplots. Identify any outliers as defined in Part 2 of this section.Exercise 33Use the same scale to construct boxplots for the pulse rates of males and females from Data Set 1 "Body Data" in Appendix B.Data Set 1
For the Verizon airport data speeds (Mbps) listed in Data Set 32 "Airport Data Speeds" in Appendix B, the highest speed of 77.8 Mbps was measured at Atlanta's (ATL) international airport. The complete list of 50 Verizon data speeds has a mean of xÌ… = 17.60 Mbps and a standard deviation
Repeat the preceding exercise using the Verizon data speed of 0.8 Mbps at Philadelphia International Airport (PHL). Preceding Exercise a. What is the difference between Verizon's data speed at Atlanta's international airport and the mean of all of Verizon's data speeds? b. How many standard
Pulse rates of adult females are listed in Data Set 1 "Body Data" in Appendix B. The lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is xÌ… = 74.0 beats per minute, and their standard deviation is s = 12.5 beats per minute.Data Set 1a. What is the difference
Data Set 31 "Garbage Weight" in Appendix B lists weights (lb) of plastic discarded by households. The highest weight is 5.28 lb, the mean of all of the weights is x̅ = 1.911 lb, and the standard deviation of the weights is s = 1.065 lb. a. What is the difference between the weight of 5.28 lb and
Listed below are prediction errors (minutes) that are differences between actual eruption times and predicted eruption times. Positive numbers correspond to eruptions that occurred later than predicted, and negative numbers correspond to eruptions that occurred before they were predicted. (The data
Using the sample data from Exercise 1, find the z score corresponding to the prediction error of 0 min. Is that prediction error significantly low or high? Why or why not? Exercise 1 4 -7 0 1 -1 1 -4 -7 22 7 -5 1
Using the same prediction errors listed in Exercise 1, construct a boxplot and include the values of the 5-number summary. Exercise 1 4 -7 0 1 -1 1 -4 -7 22 7 -5 1
In an analysis of activities that resulted in brain injuries presenting at hospital emergency rooms, the following activities were identified by the codes shown in parentheses: bicycling (12); football (14); playground (22); basketball (27); swimming (40). Find the mean of 12, 14, 22, 27, and 40.
The birth weights of a sample of males have a mean of 3272.8 g and a standard deviation of 660.2 g. The birth weights of a sample of females have a mean of 3037.1 g and a standard deviation of 706.3 g (based on Data Set 4 "Births" in Appendix B). When considered among members of the same gender,
Listed below are platelet counts (1000 cells/ μL) from subjects included in Data Set 1 "Body Data." Identify the outlier and then comment on the effect it has on the mean and standard deviation by finding the values of those statistics with the outlier included and then with the outlier
Shown below is a boxplot of a sample of 30 maximal skull breadths (mm) measured from Egyptian skulls from around 4000 B.C. What do the numbers in the boxplot represent?
Listed below are measured amounts (mg per serving) of arsenic in a sample of servings of brown rice [data from the Food and Drug Administration (FDA)]. Construct a frequency distribution. Use a class width of 2 mg, and use 0 mg as the lower class limit of the first class. 6.1 5.4 6.9 4.9 6.6 6.3
Use the frequency distribution from Exercise 1 to construct a histogram. Use class midpoint values for the horizontal scale. Exercise 1 6.1 5.4 6.9 4.9 6.6 6.3 6.7 8.2 7.8 1.5 5.4 7.3
Use amounts of arsenic in Exercise 1 and find the following: (a) mean; (b) median; (c) standard deviation; (d) variance; (e) range. Include the appropriate units of measurement. Exercise 1 6.1 5.4 6.9 4.9 6.6 6.3 6.7 8.2 7.8 1.5 5.4 7.3

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