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Assignment: 2.2 1. Use a stem-and-leaf plot to display the data. The dat::1 represent the heights of eruptions by a geyser. What can you conclude about the data? 105 90 110 150 140 110 98 145 120 116 136 130 Choose the correct stem-and-leaf plot. (Key: 15 I 5 = 155) 100 147 123 96 QA. OB. (.1 C. 9 0 6 8 9 0 10 035667 10 06 11 0 0 5 7 l l 0 0 7 8 12 0 0 8 12 0 0 3 5 6 6 13 0 0 13 0 0 5 7 14 0 14 0 8 15 0 15 0 What can you conclude about the data? 0 A. It appears that most eruptions have a height greater than 120. 0 B. It appears that most eruptions have a height between 11 and 13. 0 C. It appears that most eruptions have a height less than 148. 0 D. It appears that most eruptions have a height of around 120. 0 E. It appears that most eruptions have a height of around 12. 9 0 6 8 10 0 5 7 11 006 12 0 0 3 13 006 14 0 5 7 15 0 8 130 107 120 158 Assignment: 2.2 2. A back-to-back stem-and-leaf plot compares two data sets by using the same stems for each data set. Leaves for the first data set are on one side while leaves for the second data set are on the other side.The back-to-back stem-and-leaf plot shows the salaries (in thousands) of all lawyers at two small law firms. 1 Click the icon to view the plot. (a) What are the lowest and highest salaries at Law Firm A? at Law Firm B? At Law Firm A the lowest salary was $ and the highest salary was $ ------ ------ At Law Firm B the lowest salary was $ and the highest salary was $ (b) How many lawyers are in each firm? ------ There are lawyers at Law Firm A and lawyers at Law Firm B. ------ ------ (c) Compare the distribution of salaries at each law firm. What do you notice? 0 A. The salaries of both firms are identically distributed in the distribution range. 0 B. At Law Firm B the salaries tend to fall in the middle of the distribution range and at Law Firm A the salaries tend to be clustered at the far ends of the range. 0 C. At Law Firm A the salaries tend to fall in the middle of the distribution range and at Law Firm B the salaries tend to be clustered at the far ends of the range. 0 D. The salaries of both firms are clustered at the opposite ends of their distribution range. 1: More Info Key: 5 I 19I0 = $195,000 for Law Firm A and $190,000 for Law Firm B Law Firm A Law Firm B 5 1 9 1 4 9422210 48 9960 0 11 0 0 4 2212 0 225 13 2 2 5 9 14 0 4449 15 4 4 4 5 16 3 9 9 9951 0 17 1 25 55521 18 9 9987519 5 3 20 3. Match the plot with a possible description of the sample. Choose the correct answer below. () A. Waiting time (in minutes) for a sample of doctors' offices () B. Ages (in years) of a sample of residents of a retirement home 0 C. Time (in hours) spent watching TV in a day for a sample of teenagers 0 D. Top speeds (in miles per hour) of a sample of sports cars Assignment: 2.2 18 225 19 25568 20 134678 21 027779 Key 1812= 182 4. Match the plot with a possible description of the sample. Choose the correct answer below. 0 A. Time (in minutes) it takes a sample of employees to drive to work 0 B. Ages (in years) of a sample of residents of a retirement home 0 C. Highest yearly temperature ( ° F) for a sample of deserts 0 D. Grade point averages of a sample of students with finance majors Assignment: 2.2 ,( l'"'"'"l'""'"'l"'"'"'l" '""''I '), 60 70 80 90 100 Assignment: 2.2 5. Use the stem-and-leaf plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry? Key: 217 = 27 2 7 3 4 4 1 2 2 5 6 6 7 5 0 1 1 2 3 3 3 4 4 4 4 5 6 6 8 9 6 7 7 7 7 3 7 7 8 4 Choose the correct actual data entries below. 0 A. 27, 34, 41, 42, 42, 45, 46, 46, 47, 50, 51, 51, 52, 53, 53, 53, 54, 54, 54, 54, 55, 56, 56, 58, 59, 67, 67, 67, 73, 77, 77, 84 () B. 2.7, 3.4, 4.1, 4.2, 4.5, 4.6, 4.7, 5.0, 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.8, 5.9,6.7, 7.3, 7.7, 8.4 0 C. 2.7, 3.4, 4.1, 4.2, 4.2, 4.5, 4.6, 4.6, 4.7, 5.0, 5.1, 5.1, 5.2, 5.3, 5.3, 5.3, 5.4, 5.4, 5.4, 5.4, 5.5, 5.6, 5.6, 5.8, 5.9, 6.7, 6.7, 6.7, 7.3, 7.7, 7.7, 8.4 () D. 27, 34, 41, 42, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 58, 59, 67, 73, 77, 84 The maximum data entry is ----- The minimum data entry is ----- Assignment: 2.2 6. Use the dot plot to list the actual data entries. What is the maximum data entry? What is the minimum data entry? • • • • • • • • • • • • • • • < I I I I I I 1 1 I), 10 11 12 131415161718 Choose the correct actual data entries below. 0 A. 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 14, 15, 15, 16, 17 QB. 111, 112, 113, 114, 115, 116,117,211, 212, 213, 215, 312, 313, 413, 513 0 C. 1.1, 1.1, 1.2, 1.2, 1.2, 1.3, 1.3, 1.3, 1.3, 1.3, 1.4, 1.5, 1.5, 1.6, 1.7 0 D. 11, 12, 13, 14, 15, 16, 17 The maximum data entry is ------ The minimum data entry is ------ Assignment: 2.2 7. The data represents the actual high temperature for 14 consecutive days. 75 70 Construct a dotplot of the actual high temperatures. What does the dotplot suggest about the 65 distribution of the high temperatures? 80 55 Which plot represents a dotplot of the data? QA. (,'l B. I ' I ' ' ' ' I I ' T ' ' I ' I 50 60 70 80 90 50 60 70 80 90 oc. () D. I I I ' I ' ' ' ' ' I I ' ' ' ' ' I ' I 50 60 70 80 90 50 60 70 80 90 What does the dotplot suggest about the distribution of the high temperatures? 0 A. The actual high temperatures range from 55 degrees to 85 degrees with most readings in the 65-80 degree range. 0 8. The actual high temperatures range from 55 degrees to 85 degrees with most readings less than 55 degrees. 0 C. The actual high temperatures range from 55 degrees to 85 degrees with most readings greater than 85 degrees. 0 D. The actual high temperatures range from 55 degrees to 85 degrees with most readings in the 55-70 degree range. 75 70 70 75 65 65 75 75 85 Assignment: 2.3 1. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The mean is the measure of central tendency most likely to be affected by an extreme value (outlier). Choose the correct answer below. 0 A. True. 0 B. False. The median is the measure of central tendency most likely to be affected by an extreme value (outlier). 0 C. False. The mode is the measure of central tendency most likely to be affected by an extreme value (outlier). 2. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. Some quantitative data sets do not have medians. Choose the correct answer below. 0 A. The statement is true. 0 B. The statement is false. Some quantitative data sets have more than one median. 0 C. The statement is false. Some quantitative data sets do not have means. 0 D. The statement is false. All quantitative data set have medians. 3. Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A data set can have the same mean, median, and mode. Choose the correct answer below. 0 A. The statement is true. 0 B. The statement is false. A data set cannot have the same mean and mode. 0 C. The statement is false. A data set cannot have the same median and mode. 0 D. The statement is false. A data set cannot have the same mean and median. 4. Determine whether the approximate shape of the distribution in the histogram is symmetric, uniform, skewed left, skewed right, or none of these. Choose the best answer below. 0 A. Uniform QB. Symmetric () C. Skewed left () D. Skewed right OE. None of these 20 10 0 5. Determine whether the approximate shape of the distribution in the histogram is y symmetric, uniform, skewed left, skewed right, or none of these. 20 10 0 Choose the best answer below. QA. Skewed left 0 B. Symmetric oc. Skewed right () D. Uniform () E. None of these 6. The number of credits being taken by a sample of 13 full-time college students are listed below. Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why. 7 9 10 10 7 6 6 6 8 6 6 6 7 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The mean is ------ {Type an integer or decimal rounded to one decimal place as needed.) !_ 8. The data set does not have a mean. Does the mean represent the center of the data? 0 A. The mean represents the center. 0 8. The mean does not represent the center because it is the largest data value. 0 C. The mean does not represent the center because it is the smallest data value. 0 D. The mean does not represent the center because it is not a data value. 0 E. The data set does not have a mean. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The median is ------ (Type an integer or decimal rounded to one decimal place as needed.) () 8. The data set does not have a median. Does the median represent the center of the data? C) A. The median represents the center. 0 8. The median does not represent the center because it is the smallest data value. 0 C. The median does not represent the center because it is the largest data value. 0 D. The median does not represent the center because it is not a data value. 0 E. The data set does not have a median. Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The mode(s) is/are ------ (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) 0 8. The data set does not have a mode. Does (Do) the mode(s) represent the center of the data? 0 A. The mode(s) represent(s) the center. 0 8. The mode(s) does (do) not represent the center because it (one) is the largest data value. 0 C. The data set does not have a mode. 0 D. The mode(s) does {do) not represent the center because it (one) is the smallest data value. CJ E. The mode(s) does (do) not represent the center because it {they) is (are) not a data value. 7. The stem-and-leaf plot of weights (in pounds) of carry-on luggage on a plane is shown below. Find the mean, median, and mode of the data. If any measure cannot be found or does not represent the center of the data, explain why. 1 03 Key: 1 IO= 10 2 1477 3 78 4 1 5 5 5 07 6 5 7 8 9 10 6 Find the mean. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The mean is ------ (Type an integer or decimal rounded to one decimal place as needed.) 0 B. There is no mean for this data set. Does the mean represent the center of the data? 0 A. The mean represents the center. 0 B. The mean does not represent the center because it is not a data value. 0 C. The mean does not represent the center because it is the largest data value. 0 D. The mean does not represent the center because it is the smallest data value. 0 E. The data set has no mean because the data values are at the nominal level of measurement. Find the median. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The median is ------ (Type an integer or decimal rounded to one decimal place as needed.) 0 B. There is no median for this data set. Does the median represent the center of the data? 0 A. The median represents the center. 0 B. The median does not represent the center because it is not a data value. 0 C. The median does not represent the center because it is the largest data value. 0 D. The median does not represent the center because it is the smallest data value. 0 E. The data set has no median because the data values are at the nominal level of measurement. Find the mode(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 A. The mode(s) is/are ------ (Type an integer or decimal rounded to one decimal place as needed. Use a comma to separate answers as needed.) 0 B. There is no mode for this data set. Does (Do) the mode(s) represent typical, or central, data entries? 0 A. Yes, the mode(s) represent(s) typical data entries. () B. The mode(s) does (do) not represent typical data entries because it (one) is the smallest data value. 0 C. The mode(s) does (do) not represent typical data entries because it (they) is (are) not a data value. 0 D. The mode(s) does (do) not represent typical data entries because it (one) is the largest data value. 0 E. The data set has no mode because the data values are at the nominal level of measurement. 8. Without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning. Heart Rates of a Sample of Adults 50 G' 40 􀁪 30 5- 20 J: 10 0 55 60 65 70 75 80 85 Heart Rate (beats per minute) Choose the correct answer below. 0 A. The mean is the best measure because the data are approximately symmetric. 0 B. The median is the best measure because the data are skewed. 0 C. The mean is the best measure because there are outliers and the data is skewed. 0 D. The mode is the best measure because the data are at the nominal level of measurement. 9. The scores and their percent of the final grade for a statistics student are given. What is the student's weighted mean score? Homework The student's weighted mean score is ------ (Simplify your answer. Round to two decimal places as needed.) Quiz Quiz Project Final Exam Score 89 80 93 96 90 Percent of final grade 20 10 10 25 35 10. A student receives the following grades, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student's weighted mean grade point score? B in 2 two-credit classes D in 1 three-credit class A in 1 three-credit class C in 1 two-credit class Mean grade point score is ______ · (Round to the nearest tenth as needed.) 11. The heights (in inches) of 20 female students in a physical education class are shown below. Approximate the mean height of students in a class. Height Frequency (in inches) 60 - 62 3 63 - 65 5 66 - 68 10 69 - 71 2 12. The numbers of days 20 patients remained hospitalized are shown below. 6 9 7 14 4 5 8 8 4 11 10 6 8 6 5 7 6 6 3 11 Construct a frequency distribution and a frequency histogram of the data using 6 classes. Describe the shape of the histogram as symmetric, uniform, negatively skewed, positively skewed, or none of these. The mean height is ______ inches. (Round to the nearest inch as needed.) Construct a frequency distribution of the data using 6 classes. Class Frequency Midpoi Choose the com􀁋ct histogram below. 0 A. OB. 10 8 6 4 2 o,--.􀀕--..--- 3.5 9.5 Hospitalization 10 8 6 4 2 Frequency o,.....,..........,....,.. 3.5 9.5 Hospitalization oc. OD. 10 8 6 4 2 Frequency o􀀖........,.,...........,► 3.5 9.5 Hospitalization 10 8 6 4 2 o􀀇.........,., ......... .........,,.. 3.5 9.5 Hospitalization Describe the shape of the histogram. Choose the correct answer below. 0 A. Positively skewed () B. Negatively skewed 0 C. Uniform 0 D. Symmetric 0 E. None of these 13. During a quality assurance check, the actual coffee content (in ounces) of six jars of instant coffee was recorded as 6.03, 5.63, 6.50, 6.01, 5.99, and 6.02. (a) Find the mean and the median of the coffee content. (b) The third value was incorrectly measured and is actually 6.05. Find the mean and median of the coffee content again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error? (a) The mean coffee content is ounces. ------ (Round to three decimal places as needed.) The median coffee content is ounces. ------ (Round to three decimal places as needed.) (b) After correcting the data error, the mean coffee content is ounces. (Round to three decimal places as needed.) After correcting the data error, the median coffee content is ounces. ------ (Round to three decimal places as needed.) (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error? 0 Median 0 Mean 14. The distances (in yards) for nine holes of a golf course are listed below. 336 392 409 522 146 504 177 377 359 Complete parts (a) through (d) below. (a) Find the mean and median of the data. The mean of the data is The median of the data is (b) Convert the distances to feet. Then rework part (a). The mean of the data in feet is The median of the data in feet is (c) Compare the measures you found in part (b) with those found in part (a). What do you notice? 0 A. The mean and median in part (b) are not the mean and median in part (a) expressed in feet. 0 B. The ratio of the mean in part (b) to the mean in part (a) is not equal to the similar ratio of the medians. 0 C. The difference between the mean in part (b) and the mean in part (a) is equal to the similar difference between the medians. 0 D. The mean and median in part (b) are three times the mean and median in part (a). (d) Use your results from part (c) to explain how to quickly find the mean and median of the given data set when the distances are converted to inches. 0 A. If you multiply the mean and median from part (b) by 12, you will get the mean and median of the data set in inches. 0 B. If you multiply the mean and median from part (a) by 3, you will get the mean and median of the data set in inches. O C. If you convert all the distances to feet and then rework part (a), it will be the quickest way to obtain the mean and the median in inches. () D. If you multiply the mean and median from part (a) by 12, you will get the mean and median of the data set in inches. 15. Students in an experimental psychology class did research on depression as a sign of stress. A test was administered to a sample of 30 students. The scores are given. Complete parts (a) through (c) below. 45 33 49 38 44 43 27 39 12 11 54 21 (a) Find the mean and median of the data. 21 29 58 51 32 34 54 55 17 The mean is . (Round to three decimal places as needed.) ------ The median is . (Type an integer or a decimal.) ------ (b) Draw a stem-and-leaf plot for the data using one row per stem. Which stem-and-leaf plot below shows the data? () A. l 69 () B. l I 1244789 ()C. l 112457789 2 1359 2 123445789 2 13457 3 1134589 3 I 134579 3 16 4 123445788 4 1358 4 13459 5 11244777 5 67 5 123447889 (c) Describe the shape of the distribution. Which description below best describes the shape of the distribution? 0 A. The distribution is skewed left (negatively skewed). 0 B. The distribution is skewed right (positively skewed). 0 C. The distribution is symmetric. 0 D. The distribution is uniform. 16 47 38 QD. 14 41 23 l 124567 2 111379 3 234889 4 134579 5 144578 15 21 57 1. Find the range of the data set represented by the graph . • • • • • • •• • .x •••• •• • •• •••• I ' ' ' ' I ' ' ' I ' ' ' ' I ' ' ' I ' ' ' ' I ' ' ' ' I 70 75 80 8 5 90 9 5 100 The range of the data set is . (Simplify your answer.) ------ Assignment: 2.4 2. Both data sets have a mean of 245. One has a standard deviation of 16, and the other has a standard deviation of 24. 1 Click the icon to view data sets. Which data set has which deviation? 0 A. (a) has a standard deviation of 24 and (b) has a standard deviation of 16, because the data in (a) have more variability. 0 B. (a) has a standard deviation of 16 and (b) has a standard deviation of 24, because the data in (b) have less variability. 1: Data Table (a) 20 8 9 Key: 20 I 8 = 208 (b) 20 21 3 5 8 21 1 22 1 1 22 2 3 5 23 0 0 6 7 23 0 3 5 7 8 24 3 5 7 24 1 1 2 3 3 3 25 1 3 6 8 25 1 5 8 8 26 0 9 9 26 2 3 4 5 27 7 27 0 9 28 3 5 7 28 3. Compare the three data sets on the right. (i) Ci' C Q) ::, CY 7 ii ii II II II II IIL _J■I 0-1-'"11 ___ ,..... 3 45 67 891011 Data value (ii) Ci' C <ll ::, CY 7 _JL .... 11■1 11■1 11■1 0--1-...,.11,11.,....,.......􀁆 34567891011 Data value d25 d36 (a) Which data set has the greatest sample standard deviation? (iii) 0 A. Data set (ii), because it contains the greater number of entries. :,.. (.) C Q) ::, rr @ u.. 7 o..U....,.i,i,iJ􀀅 3 45 67891011 Data value 0 B. Data set (i), because it has more entries that are farther away from the mean. 0 C. Data set (iii), because its data have more variability. Which data set has the least sample standard deviation? 0 A. Data set (iii) because it has more entries near the mean than far away from it. () B. Data set (ii), because it has more entries that are close to the mean. () C. Data set (i), because it has no entries near the mean. (b) How are the data sets the same? How do they differ? 0 A. The three data sets have the same mean but have different standard deviations. 0 B. The three data sets have the same range but have different means. 0 C. The three data sets have the same standard deviations but have different ranges. () D. The three data sets have the same range and mean but have different standard deviations. 4. Compare the (i) three data sets on the right. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,( I I I I I I I), 10111213141516 (ii) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,( I I I I I I I), 10111213141516 (a) Which data set has the greatest sample standard deviation? (iii) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ,( l I I I I I I), 10111213141516 0 A. Data set (iii), because it has more entries that are farther away from the mean. () B. Data set (ii), because it has two entries that are far away from the mean. 0 C. Data set (i), because it has more entries that are close to the mean. Which data set has the least sample standard deviation? 0 A. Data set (iii), because it has more entries that are farther away from the mean. 0 B. Data set (i), because it has more entries that are close to the mean. () C. Data set (ii), because it has less entries that are farther away from the mean. (b) How are the data sets the same? How do they differ? () A. The three data sets have the same mode but have different standard deviations and means. 0 B. The three data sets have the same mean and mode but have different medians and standard deviations. 0 C. The three data sets have the same standard deviations but have different means. 0 D. The three data sets have the same mean, median and mode but have different standard deviations. 5. Heights of men on a baseball team have a bell-shaped distribution with a mean of 186 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of the men between the following values? a. 172 cm and 200 cm b. 179 cm and 193 cm a. ______ % of the men are between 172 cm and 200 cm. (Round to one decimal place as needed.) b. % of the men are between 179 cm and 193 cm. (Round to one decimal place as needed.) 6. The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $100. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 76. (a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1500 and $1700. farms (Round to the nearest whole number as needed.) ------ (b) If 23 additional farms were sampled, about how many of these additional farms would you expect to have land and building values between $1500 per acre and $1700 per acre? farms out of 23 (Round to the nearest whole number as needed.) ------ 7. The mean value of land and buildings per acre from a sample of farms is $1700, with a standard deviation of $100. The data set has a bell-shaped distribution. Using the empirical rule, determine which of the following farms, whose land and building values per acre are given, are unusual (more than two standard deviations from the mean). Are any of the data values very unusual (more than three standard deviations from the mean)? $1758 $1944 $1698 $1307 $1782 $1634 Which of the farms are unusual (more than two standard deviations from the mean)? Select all that apply. □ A. $1634 □ B. $1698 □ c. $1782 0D. $1307 □ E. $1944 0 F. $1758 Which of the farms are very unusual (more than three standard deviations from the mean)? Select all that apply. 0 A. $1782 0 8. $1307 0 C. $1944 0 D. $1698 0 E. $1758 0 F. $1634 D G. None of the data values are very unusual. 8. Sample annual salaries (in thousands of dollars) for employees at a company are listed. 40 52 50 51 33 33 40 52 50 32 51 40 44 (a) Find the sample mean and sample standard deviation. (b) Each employee in the sample is given a 5% raise. Find the sample mean and sample standard deviation for the revised data set. (c) To calculate the monthly salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. (d) What can you conclude from the results of (a), (b), and (c)? (a) The sample mean is x = thousand dollars. ------ (Round to one decimal place as needed.) T he sample standard deviation is s = ______ thousand dollars. (Round to one decimal place as needed.) (b) The sample mean is x = ______ thousand dollars. (Round to one decimal place as needed.) The sample standard deviation is s = ______ thousand dollars. (Round to one decimal place as needed.) (c) The sample mean is x = ______ thousand dollars. (Round to one decimal place as needed.) The sample standard deviation is s = ______ thousand dollars. (Round to one decimal place as needed.) (d) What can you conclude from the results of (a), (b), and (c)? 0 A. When each entry is multiplied by a constant k, the new sample mean is k • x and the sample standard deviation remains unaffected. 0 B. When each entry is multiplied by a constant k, the sample mean and the sample standard deviation remain unaffected. () C. When each entry is multiplied by a constant k, the new sample standard deviation is k • s and the sample mean remains unaffected. 0 D. When each entry is multiplied by a constant k, the new sample mean is k • x and the new sample standard deviation is k • s. Assignment: 2.5 1. A student's score on an actuarial exam is in the 78th percentile. What can you conclude about the student's exam score? Choose the correct answer below. 0 A. About 78% of students achieved the same score as this particular student. 0 B. 78% of students scored higher than this particular student. 0 C. The student scored a 78% on the exam. 0 D. The student scored higher than 78% of the students who took the actuarial exam. 2. Use the box-and-whisker plot to identify the five-number summary. Min = Max= 11 13 15 17 - 22 12 14 16 18 20 22 3. (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 3 7 7 5 2 9 8 6 9 5 9 3 2 5 2 9 8 6 6 9 (a) Min = (Simplify your answer.) ------ 01 = (Simplify your answer. Do not round.) ------ 02 = (Simplify your answer. Do not round.) ------ 03 = (Simplify your answer. Do not round.) ------ Max= (Simplify your answer.) ------ (b) Choose the correct box-and-whisker plot below. () A. 0 B. m -ffi ,(I ' I ' I ' I' )o <(I ' I I I I I ' ➔ 2 4 6 8 2 4 6 8 () C. ffi ,( I I I I I I I I ➔ 2 4 6 8 (JD. ffi ,( I I I I I I I I ➔ 2 4 6 8 4. (a) Find the five-number summary, and (b) draw a box-and-whisker plot of the data. 4 8 8 6 2 9 8 7 9 6 9 5 2 6 2 9 8 7 7 9 (a) Min = (Simplify your answer.) ------ 01 = (Simplify your answer. Do not round.) ------ 02 = (Simplify your answer. Do not round.) ------ 03 = (Simplify your answer. Do not round.) ------ Max = (Simplify your answer.) ------ (b) Choose the correct box-and-whisker plot below. ,( I I I I I ➔ 3 5 7 9 () B. --m ('. I I I I I I I I )I 2 4 6 8 oc. --EE- ,('. I I I I I ➔ 3 5 7 9 5. Use the box-and-whisker plot to determine if the shape of the distribution represented is symmetric, skewed left, skewed right, or none of these. Choose the correct answer below. QD. -EB ,('. I I 4 6 I ,> 0 none of these 0 skewed left 0 skewed right · I I I • 0 symmetric o-􀀅􀀆􀀇-􀀈􀀉􀀊􀀆􀀇-􀀋􀀌 40 80 120 160 200 6. A certain brand of automobile tire has a mean life span of 32,000 miles and a standard deviation of 2,350 miles. (Assume the life spans of the tires have a bell-shaped distribution.) (a) The life spans of three randomly selected tires are 35,000 miles, 36,000 miles, and 31,000 miles. Find the z-score that corresponds to each life span. For the life span of 35,000 miles, z-score is ------ (Round to the nearest hundredth as needed.) For the life span of 36,000 miles, z-score is ------ (Round to the nearest hundredth as needed.) For the life span of 31,000 miles, z-score is ------ (Round to the nearest hundredth as needed.) According to the z-scores, would the life spans of any of these tires be considered unusual? Q No 0 Yes (b) The life spans of three randomly selected tires are 27,300 miles, 36,700 miles, and 32,000 miles. Using the empirical rule, find the percentile that corresponds to each life span. The life span 27,300 miles corresponds to the th percentile. ------ The life span 36,700 miles corresponds to the th percentile. The life span 32,000 miles corresponds to the th percentile. 7. A modified boxplot is a boxplot that uses symbols to identify outliers. The horizontal line of a modified boxplot extends as far as the minimum data entry that is not an outlier and the maximum data entry that is not an outlier. (a) Identify any outliers and (b) draw a modified box plot that represents the data set. Use a cross ( x) to plot any outliers. 95 60 43 77 31 54 52 39 88 63 51 61 50 8 42 49 87 62 (a) Identify any possible outliers. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. L A. The outlier(s) is(are) ------ (Type an integer or decimal. Use a comma to separate answers as needed.) () B. There are no outliers. (b) Choose the correct boxplot of the data below. QA. ()B. oc. OD. • 8· -0---x ,( I ' I I I ' I ' I I I I > ,( I ' I I I I I I I ' I I > ,(I• I' I• I• I• I•), ,( I I I ' I I I ' I ' I ' ), 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Assignment: 3.1 1. Determine which numbers could not be used to represent the probability of an event. Select all that apply. 320 DA. --, because probability values cannot be in fraction form. 1058 D B. - 1.5, because probability values cannot be less than 0. D C. 33.3%, this is because probability values cannot be greater than 1. 64 D D. -, because probability values cannot be greater than 1. 25 D E. 0, because probability values must be greater than 0. D F. 0.0002, because probability values must be rounded to two decimal places. 2. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 160? Choose the correct probability below. OA. 0.95 OB. 0.05 oc. 0.25 0 D. 0 3. Thirteen of the 50 digital video recorders (DVRs) in an inventory are known to be defective. What is the probability you randomly select an item that is not defective? The probability is ------ (Do not round.) 4. Identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Randomly choosing an odd number between 1 and 9, inclusive The sample space is { }. ------ (Use a comma to separate answers as needed. Use ascending order.) There are outcome(s) in the sample space. ------ 5. The access code for a car's security system consists of five digits. The first digit cannot be 1 and the last digit must be odd. How many different codes are available? The number of different codes available is ------ (Type a whole number.) 6. A probability experiment consists of rolling a 6-sided die. Find the probability of the event below. rolling a number less than 4 The probability is ------ (Type an integer or decimal rounded to three decimal places as needed.) 7. An individual stock is selected at random from the portfolio represented by the box-and-whisker l I l • • plot shown to the right. Find the probability that the stock price is (a) 14 22 31 50 95 X less than $22, (b) between $22 and $50, and (c) $31 or more. 10 20 30 40 50 60 70 80 90 100 (a) The probability that the stock price is less than $22 is . (Do not round.) ------ (b) The probability that the stock price is between $22 and $50 is . (Do not round.) ------ (c) The probability that the stock price is $31 or more is . (Do not round.) ------ 8. Use the bar graph below, which shows the highest level of education received by employees of a company, to find the probability that the highest level of education for an employee chosen at random is E. The probability that the highest level of education for an employee chosen at random is E is ------ (Round to the nearest thousandth as needed.) Level of education 9. Use the frequency distribution to the right, which shows the number of voters (in millions) according to age, to find the probability that a voter chosen at random is in the given age range. not between 25 and 34 years old The probability is ------ (Round to three decimal places as needed.) Ages of voters Frequency 18 to 20 5.3 21 to 24 10.5 25 to 34 24.3 35 to 44 22.1 45 to 64 56.9 65 and over 28.4 Assignment: 3.2 1. For the given pair of events, classify the two events as independent or dependent. Finding that your cell phone works Finding that your dvd player works Choose the correct answer below. 0 A. The two events are dependent because the occurrence of one does not affect the probability of the occurrence of the other. 0 B. The two events are dependent because the occurrence of one affects the probability of the occurrence of the other. 0 C. The two events are independent because the occurrence of one affects the probability of the occurrence of the other. 0 D. The two events are independent because the occurrence of one does not affect the probability of the occurrence of the other. 2. In the general population, one woman in eight will develop breast cancer. Research has shown that 1 woman in 650 carries a mutation of the BRCA gene. Nine out of 10 women with this mutation develop breast cancer. (a) Find the probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene. The probability that a randomly selected woman will develop breast cancer given that she has a mutation of the BRCA gene is ------ (Round to one decimal place as needed.) (b) Find the probability that a randomly selected woman will carry the mutation of the BRCA gene and will develop breast cancer. The probability that a randomly selected woman will carry the gene mutation and develop breast cancer is (Round to four decimal places as needed.) (c) Are the events of carrying this mutation and developing breast cancer independent or dependent? 0 Independent 0 Dependent ------ 3. A study found that 35% of the assisted reproductive technology (ART) cycles resulted in pregnancies. Twenty-eight percent of the ART pregnancies resulted in multiple births. (a) Find the probability that a random selected ART cycle resulted in a pregnancy and produced a multiple birth. (b) Find the probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth. (c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain. (a) The probability that a randomly selected ART cycle resulted in a pregnancy and produced a multiple birth is (Round to the nearest thousandth as needed.) (b) The probability that a randomly selected ART cycle that resulted in a pregnancy did not produce a multiple birth is (Round to the nearest thousandth as needed.) (c) Would it be unusual for a randomly selected ART cycle to result in a pregnancy and produce a multiple birth? Explain. Choose the correct answer below. 0 A. Yes, this is unusual because the probability is less than or equal to 0.05. 0 B. No, this is not unusual because the probability is less than or equal to 0.05. 0 C. No, this is not unusual because the probability is not less than or equal to 0.05. C) D. Yes, this is unusual because the probability is not less than or equal to 0.05. 4. Suppose 90% of kids who visit a doctor have a fever, and 25% of kids with a fever have sore throats. What's the probability that a kid who goes to the doctor has a fever and a sore throat? The probability is ------ (Round to three decimal places as needed.) 5. The table below shows the results of a survey in which 143 men and 145 women workers ages 25 to 64 were asked if they have at least one month's income set aside for emergencies. Complete parts (a) through (d). Men Women Total Less than one month's income 66 83 149 One month's income or more 77 62 139 Total 143 145 288 (a) Find the probability that a randomly selected worker has one month's income or more set aside for emergencies. The probability is . (Round to the nearest thousandth as needed.) ------ (b) Given that a randomly selected worker is a male, find the probability that the worker has less than one month's income. The probability is . (Round to the nearest thousandth as needed.) ------ (c) Given that a randomly selected worker has one month's income or more, find the probability that the worker is a female. The probability is . (Round to the nearest thousandth as needed.) ------ (d) Are the events "having less than one month's income saved" and "being male" independent or dependent? 0 Dependent C Independent 6. The probability that a person in the United States has type B+ blood is 12%. Five unrelated people in the United States are selected at random. Complete parts (a) through (d). (a) Find the probability that all five have type B+ blood. The probability that all five have type B+ blood is ------ (Round to six decimal places as needed.) (b) Find the probability that none of the five have type B+ blood. The probability that none of the five have type B+ blood is ------ (Round to three decimal places as needed.) (c) Find the probability that at least one of the five has type B+ blood. The probability that at least one of the five has type B+ blood is ------ (Round to three decimal places as needed.) (d) Which of the events can be considered unusual? Explain. Select all that apply. 0 A. The event in part (b) is unusual because its probability is less than or equal to 0.05. 0 8. The event in part (a) is unusual because its probability is less than or equal to 0.05. 0 C. The event in part (c) is unusual because its probability is less than or equal to 0.05. C.J D. None of these events are unusual. 7. By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B I A)= P( \::􀁤 B) . Use the information below to find the probability that a flight departed on time given that it arrives on time. The probability that an airplane flight departs on time is 0.89. The probability that a flight arrives on time is 0.87. The probability that a flight departs and arrives on time is 0.81. The probability that a flight departed on time given that it arrives on time is (Round to the nearest thousandth as needed.) ------ 8. By rewriting the formula for the Multiplication Rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P( BI A)= P(A and B) . Use the information below to find the probability that a flight arrives on time given that it departed P(A) on time. The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.88. The probability that a flight departs and arrives on time is 0.83. The probability that a flight arrives on time given that it departed on time is (Round to the nearest thousandth as needed.) ------ 1. Decide if the events are mutually exclusive. Event A: Randomly selecting someone treated with a certain medication Event B: Randomly selecting someone who received no medication Are the two events mutually exclusive? Assignment: 3.3 0 A. Yes, because someone treated with medication can have received no medication. 0 B. Y es, because someone treated with medication cannot have received no medication. 0 C. No, because someone treated with medication can have received no medication. 0 D. No, because someone treated with medication cannot have received no medication. 2. A company that makes cartons finds that the probability of producing a carton with a puncture is 0.07, the probability that a carton has a smashed corner is 0.09, and the probability that a carton has a puncture and has a smashed corner is 0.006. Answer parts (a) and (b) below. (a) Are the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" mutually exclusive? Explain. 0 A. Yes, a carton cannot have a puncture and a smashed corner. 0 B. No, a carton can have a puncture and a smashed corner. 0 C. Yes, a carton can have a puncture and a smashed corner. 0 D. No, a carton cannot have a puncture and a smashed corner. (b) If a quality inspector randomly selects a carton, find the probability that the carton has a puncture or has a smashed corner. The probability that a carton has a puncture or a smashed corner is ------ (Type an integer or a decimal. Do not round.) 3. A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a heart or club. (b) Compute the probability of randomly selecting a heart or club or spade. (c) Compute the probability of randomly selecting a seven or heart. a. P(heart or club)= ______ (Round to three decimal places as needed.) b. P(heart or club or spade)= ______ (Round to three decimal places as needed.) c. P(seven or heart)= ______ (Round to three decimal places as needed.) 4. T he table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d). Nursing majors Males 98 Females 600 Total 698 Non-nursing majors 1012 1729 2741 Total 1110 2329 3439 (a) Find the probability that the student is male or a nursing major. P(being male or being nursing major)= ------ (Round to the nearest thousandth as needed.) (b) Find the probability that the student is female or not a nursing major. P(being female or not being a nursing major)= ------ (Round to the nearest thousandth as needed.) (c) Find the probability that the student is not female or a nursing major. P(not being female or being a nursing major)= ------ (Round to the nearest thousandth as needed.) (d) Are the events "being male" and "being a nursing major" mutually exclusive? Explain. 0 A. No, because there are 98 males majoring in nursing. 0 B. No, because one can't be male and a nursing major at the same time. 0 C. Yes, because there are 98 males majoring in nursing. 0 D. Yes, because one can't be male and a nursing major at the same time. 5. The table below shows the results of a survey that asked 2856 people whether they are involved in any type of charity work. A person is selected at random from the sample. Complete parts (a) through (e). Male Female Total Frequently 224 208 432 Occasionally 457 430 887 Not at all 793 744 1537 Total 1474 1382 2856 (a) Find the probability that the person is frequently or occasionally involved in charity work. P(being frequently involved or being occasionally involved)= ------ (Round to the nearest thousandth as needed.) (b) Find the probability that the person is female or not involved in charity work at all. P(being female or not being involved)= ------ (Round to the nearest thousandth as needed.) (c) Find the probability that the person is male or frequently involved in charity work. P(being male or being frequently involved)= ------ (Round to the nearest thousandth as needed.} (d) Find the probability that the person is female or not frequently involved in charity work. P(being female or not being frequently involved)= ------ (Round to the nearest thousandth as needed.) (e) Are the events "being female" and "being frequently involved in charity work" mutually exclusive? Explain. 0 A. Yes, because no females are frequently involved in charity work. 0 B. No, because no females are frequently involved in charity work. <􀁔 C. No, because 208 females are frequently involved in charity work. 0 D. Yes, because 208 females are frequently involved in charity work. 6. The number of responses to a survey are shown in the Pareto chart. The survey asked 1028 adults how they would grade the quality of their public schools. Each person gave one response. Find each probability. (a) Randomly selecting a person from the sample who did not give the public schools an A (b) Randomly selecting a person from the sample who gave the public schools a grade better than a D (c) Randomly selecting a person from the sample who gave the public schools a Dor an F (d) Randomly selecting a person from the sample who gave the public schools an A or B 400 354 c§ 300 252 235 ,n 200 100 ::, z D B 120 F Response (a) The probability that a randomly selected person did not give the public schools an A is ------ (Round to three decimal places as needed.) (b) The probability that a randomly selected person gave the public schools a grade better than a D is 67 A ------ (Round to three decimal places as needed.) (c) The probability that a randomly selected person gave the public schools a Dor an F is ------ (Round to three decimal places as needed.) (d) The probability that a randomly selected person gave the public schools an A or B is ------ (Round to three decimal places as needed.) 7. The percent distribution of a person's accumulating specific amounts of credit card charges over a 12-month period is shown in the pie chart. Find each probability. a. What is the probability that a person's total charges are $1000 or more? (Type an integer or a decimal.) ------ b. What is the probability that a person's total charges are less than $3000? (Type an integer or a decimal.) ------ c. What is the probability that a person's total charges are $500 to $2999? (Type an integer or a decimal.) ------ Credit Card Charges =■ =-:--,U- nd .,... e_r.,,.. $1 '"" 0 """0 -3= 3""" 0/4.,...., o 0 $100-$499 17% □ $500-$999 16% e $1000-$1999 13% □ $2000-$2999 6% ■ $3000-$4999 8% ■ $5000-$9999 6% n $10,000 or more 1 %

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Assignment 2.2
1)
Answer C is correct (the numbers are 90,96,98,100,105,...)
Answer C is correct (since only 150 and 158 are higher)

2) By looking at the back-to-back steam-and-leaf plot
a)
Law Firm A : 91,000$ is the lowest and 203,000$ is the highest
Law Firm B : 91,000$ is the lowest and 195,000$ is the highest
b) 30 and 32 (by counting the number of digits on each side)
c) Answer D is correct

3) By elimination, it seems to be top speeds of a sample of sports cars (answer D)

4) By elimination, it seems to be the ages (in years) of a sample residents of a retirement home (answer B)

5) By listing the numbers by keys, we see that the answer A) and the maximum is 84 (last key) and the minimum is 27 (first key)

6) By listing the numbers in the dot plot, we see the answer is A) and the maximum is 17 while the minimum is 11

7)
Answer A) represents the data since if you compute the frequency you'd have:
55 -> 1
60 -> 0
65 -> 3
70 -> 3
75 -> 5
80 -> 1
85 -> 1
Answer A) because we see most bars are in the 65-80 area of the dotplot


Assignement 2.3
This part doesn't need an explanation, this is basically the course
1) Answer A
2) Answer D...

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