Chapter 6 Review Problems

Chapter 6 Review Problems - Chapter 6 The Standard...

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Unformatted text preview: Chapter 6 The Standard Deviation as a Ruler and thre Normal Model (Review) Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use summary statistics to answer the question. 1) Here are the summary statistics for the monthly payroli for an accounting firm: iowest salary; $ 1) 15,000, mean salary : $35,000, median a $25,000, range : $60,000, IQR = $30,000, first quartile = $ 17,500, standard deviation = $20,000. Do you think the distribution of salaries is symmetric, skewed to the left, or skewed to the right? Explain why. A) Skewed to the right; mean is higher than median. B) Symmetric, mean is higher than median. C) Skewed to the left, mean is higher than median. i3) Skeweci to the left; mean is lower than median. E) Skewed to the right, mean is lower than median. 2) Here are some summary statistics for the recent English exam: iowest score = 34, mean score 2 74, 2) median 2 88.2, range 2 76, IQR = 59, Q1 = 30, standard deviation 2 8.6. Is the distribution symmetric, skewed to the left, or skewed to the right? Expiain. A) Skewed to the left, mean higher than median. B) Symmetric, mean lower than median. C) Skewed to the right, mean lower than median. D) Skewed to the left, mean lower than median. E) Skewed to the right, mean higher than median. 3) Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 3) years: lowest amount z: 10 inches, mean = 40 inches, median = 33 inches, range = 90 inches, IQR = 50, Q1 == 16, standard deviation 2 10 inches. is the distribution symmetric, skewed to the left, or skewed to the right? Expiain. A) Skewed to the right, mean lower than median. B) Symmetric, mean higher than median. C) Skewed to the left, mean iower than median. D) Skewed to the left, mean higher than median. E) Skeweci to the right, mean higher than median. 4) The speed vehicles travelled on a local highway was recorded for one month. The speeds ranged 4) from 53 mph to 68 mph with a mean speed of 54. mph and a standard deviation of 8 mph. The quartiles and median speeds were 56 mph, 65 mph, and 51 mph. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. A) Skewed to the right, mean lower than median. B) Skewed to the left, mean higher than median. C) Skewed to the left, mean iower than median. D) Skewed to the right, mean higher than median. E) Symmetric, mean higher than median. 5) Here are some summary statistics for all of the runners in a local 12K race: slowest time = 133 5) minutes, mean = 81 minutes, median = 81 minutes, range = 103 minutes, IQR = 64, Q1 = 32, standard deviation z 12 minutes. Is the distribution symmetric, skewed to the left, or skewed to the right? Explain. A) Skewed to the right, mean lower than median. B) Skewed to the left, mean tower than median. C) Skewed to the right, mean higher than median. D) Skewed to the left, mean higher than median. E) Symmetric, mean same as median. 6) Consider a data set of positive values, at ieast two of which are not equal. Which of the following 6) sample statistics will be changed when each value in this data set is multiplied by a constant Whose absolute value is greater than 1? I. The mean II. The median III. The standard deviation A) I only B) 11 oniy C) III only D) I and II only E) I, II, and III Use summary statistics to answer the question. 7) Here are the summary statistics for the monthly payroli for an accounting firm: 7) lowest salary = $30,000, mean salary : $70,000, median m $50,000, range z: $120,000, IQR r» $60,000, first quartile = $35,000, standard deviation = $40,000. Suppose that business has been good and the company gives every employee a $5000 raise. Give the new value of each of the Summary statistics. A) Minimum: 30,000; Mean: 70,000; Median: 50,000; Range: 120,000; IQR: 60,000; Q1: 40,000; SD: 40,000 B) Minimum: 35,000; Mean: 75,000; Median: 50,000; Range: 120,000; EQR: 60,000; Q1: 40,000; SD: 40,000 C) Minimum: 35,000; Mean: 70,000; Median: 55,000; Range: 120,000; IQR: 60,000; Q1: 40,000; SD: 40,000 D) Minimum: 30,000; Mean: 75,000; Median: 55,000; Range: 120,000; IQR: 60,000; Q1: 40,000; SD: 40,000 E) Minimum: 35,000; Mean: 75,000; Median: 55,000; Range: 120,000; IQR: 60,000; Q1: 40,000; SD: 40,000 8) Here are some summary statistics for the recent English exam: lowest score a 32, mean score a 66, 8) median : 80.2, range a 78, IQR n 61, Q1 :— 26, standard deviation = 8.2. Suppose the students did not study for the exam and each score went down 15%. Tell the new value for each of the summary statistics. Express your answer in exact decimals. A) Lowest score: 4.8, mean: 9.9, median: 12.03, range: 11.7, IQR: 9.15, Q1: 22, SD: 1.23 B) Lowest score: 27.2, mean: 56.1, median: 68.17, range: 78, iQR: 61, Q1: 22, SD: 6.97 C) Lowest score: 36.8, mean: 75.9, median: 92.23, range: 89.7, IQR: 70.15, Q1: 22, SD: 9.43 D) Lowest score: 27.2, mean: 56.1, median: 68.17, range: 78, IQR: 51.85, Q1: 22, SD: 6.97 E) Lowest score: 27.2, mean: 56.1, median: 68.17, range: 66.3, IQR: 51.85, Q1: 22, SD: 6.97 9) Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 9) years: lowest amount = 10 inches, mean : 42 inches, median m 35 inches, range m 90 inches, IQR : 54, Q1 7» 17, standard deviation = 8 inches. Suppose snowfall was tracked for 5 additional years and the annual snowfali was found to increase by 20%. Find the new mean and standard deviation. A) Mean: 33.6 inches, SD: 8 inches B) Mean: 33.6 inches, SD: 6.4 inches C) Mean: 50.4 inches, SD: 9.6 inches D) Mean: 50.4 inches, SD: 8 inches E) Mean: 8.4: inches, SD: 1.6 inches 10) The speed vehicies traveled on a local highway was recorded for one month. The speeds ranged 10) from 49 mph to 64 mph with a mean speed of 55 mph and a standard deviation of 8 mph. The quartiles and median speeds were 52 mph, 61 mph, and 52 mph. Suppose increased patrols reduced speeds by 7%. Find the new mean and standard deviation. Express your answer in exact decimals. A) Mean: 58.85 mph, SD: 8.56 mph B) Mean: 58.85 mph, SD: 8 mph C) Mean: 51.15 mph, SD: 7.44 mph D) Mean: 51.15 mph, SD: 8 mph E) Mean: 3.85 mph, SD: 0.56 mph 11) Here are some summary statistics for at} of the runners in a local 12K race: slowest time a 138 11) minutes, mean = 82 minutes, median x 82 minutes, range m 108 minutes, IQR m 64, Q1 2: 33, standard deviation = 15 minutes. Suppose last year‘s race results were better by 8%. Find last year’s mean and standard deviation. Express your answer in exact decimals. A) Mean: 75.44 minutes, SD: 15 minutes B) Mean: 88.56 minutes, SD: 16.2 minutes C) Mean: 75.44 minutes, SD: 13.8 minutes D) Mean: 88.56 minutes, SD: 15 minutes E) Mean: 6.56 minutes, Bi): 1.2 minutes 12) Here are the summary statistics for the monthly payroli for an accounting firm: lowest salarym 12) $30,000, mean salary = $70,000, median 2 $50,000, range =2 $120,000, EQR 2 $60,000, first quartile 2 $35,000, standard deviation = $40,000. Between what two values are the middle 50% of the salaries found? A) $35,000 and $60,000 B) $35,000 and $75,000 C) $35,000 and $95,000 D) $30,000 and $150,000 E) $70,000 and $50,000 13) Here are some summary statistics for the recent English exam: lowest score = 38, mean score = 74, 13) median “2 88.2, range 2 ’72, IQR m 61, Q1 m 30, standard deviation 2 9.8. Between what two values are the middie 50% of the scores found? A) 38 and 110 B) 30 and 91 C) 22.05 and 66.15 D) '74 and 88.2 E) 18.5 and 55.5 14) Here are some summary statistics for last years basketball team scoring output: lowest score 2 22 111) points, mean = 55 points, median a 49 points, range 2 93 points, IQR :2 50, Q1 2 22, standard deviation = ‘7 points. BetWeen what two values are the middle 50% of scores found? A) 12.25 and 36.75 B) 55 and 49 C) 13.75 and 4125 D) 22 and 72 E) 22 and 115 15) Here are some summary statistics for all of the runners in a local 12K race: slowest time n 131 15) minutes, mean m 84. minutes, median 2 84 minutes, range 2 101 minutes, IQR = 64, Q1 = 34, standard deviation 2 10 minutes. Between what two values are the middle 50% of times? A) 21 and 63 B) 34 and 98 C) 42 and 84 D) 16.8 and 67.2 E) 131 and 30 16) The speed vehicles travelled on a local highway was recorded for one month. The speeds ranged 16) from 45 mph to 60 mph with a mean speed of 57 mph and a standard deviation of 8 mph. The quartiles and median speeds were 48 mph, 57 mph, and 54 mph. Suppose during the month, one driver was clocked at 25 mph. Which of the summary statistics might not change if that data value was added to the distribution? A) Q1, Q3 B) Range, SD C) Median, range D) Median, IQR E) Mean, IQR Find the number of standard deviations from the mean. Round to the nearest hundredths 157) A town's average snowfall is 33 inches per year with a standard deviation of 11 inches. How many 17) standard deviations from the mean is a snowfall of 66 inches? A) About 0.33 standard deviations above the mean B) About 2.00 standard deviations above the mean C) About 3.00 standard deviations above the mean D) About 0.33 standard deviations below the mean B) About 3.00 standard deviations below the mean 18) The mean test score on the Chapter 7 mathematics test was 71 with a standard deviation of 13. How many standard deviations from the mean is a test score of8'7? A) About 1.23 standard deviations above the mean B) About 0.82 standard deviations above the mean C) About 0.67 standard deviations above the mean D) About 1.23 standard deviations below the mean E) About 0.67 standard deviations below the mean 19) The average number of pounds of sugar a person eats per year isé pounds with a standard deviation of 1.1 pounds. How many standard deviations from the mean is the consumption ofii pounds of sugar? A) About 1.67 standard deviations above the mean B) About 1.67 standard deviations below the mean C) About 4.55 standard deviations above the mean D) About 5.45 standard deviations above the mean B) About 4.55 standard deviations below the mean 20) The setter on your school’s volleybaii team average 50 assists per match with a standard deviation of 9. How many standard deviations from the mean is an outing with 72 assists? A) About 2.44 standard deviations beiow the mean B) About 1.22 standard deviations below the mean C) About 1.44 standard deviations below the mean D) About 1.22 standard deviations above the mean E) About 2.44 standard deviations above the mean 21) The average number of average number of hours per day a college student spends on homework is 4 hours with a standard deviation of 0.75 hours. How many standard deviations from the mean is 2 hours spent on homework? A) About 2.67 standard deviations above the mean B) About 1.33 standard deviations below the mean C) About 2.67 standard deviations below the mean D) About 2.00 standard deviations above the mean B) About 1.33 standard deviations above the mean 18) 19) 20) 21) Solve the problem. 22) A town's snowfali in December averages 13 inches with a standard deviation of8 inches while in 22) February, the average snowfall is 40 inches with a standard deviation of 13 inches. In which month is it more likely to snow 32 inches? Explain. A) December. Snowfall of 32 inches is — “Eg- from the mean while snowfall of 32 inches is 183 from the mean in February. B) It is equally likely in either month. One can‘t predict Mother Nature. C) December. Snowfall of 32 inches is g from the mean while snowfall of 32 inches is ~«- 385 from the mean in. February. D) February. Snowfall of 32 inches is — 38:; from the mean while snowfall of 32 inches is ~15 from the mean in December. E) February. Snowfall of 32 inches is is?» from the mean while snowfall of 32 inches is — {3; from the mean in December. 23) A basketball coach kept stats for his team in free throw percentage and steals (among others). A1 23) the last garne, Erin‘s free throw percentage was 79% and she had 4 steals. The team averaged 95% from the free throw line with a standard deviation of 15 and they averaged 7 steals with a standard deviation of 4. In which category did Erin do better compared. with her team? Explain. A) Steals. 4 steals is — 3: standard deviations from the mean while 79% free throw average is — 35-3—- standard deviations from the mean. 15 B) Steals. 4 steals is w %% standard deviations from the mean while 79% free throw average is — 315-- standard deviations from the mean. 4 C) One can't compare the two categories, they are too different. D) Free throw percentage. 79% free throw average is — it; standard deviations from the mean while 4 steals is w 3- standard deviations from the mean. E) Free throw percentage. 79% free throw average is “2:- standard deviations from the mean while 4 steals is - ég standard deviations from the mean. 24) Two different running shoe manufachirers market running shoes to first time marathon runners. 24) Swift ciairns a mean shoe fife of 600 miles, while Endurarnax ciairns a shoe iife of 650 miles. If the standard deviation for both shoes is 59 miies, which shoe would you purchase before starting your marathon training (where you figure to iog 500 mites)? Explain. A) Endurarnax. The Enduramax shoes have a longer mean shoe life. B) Endurarnax. Endurarnax shoes are — «jg—33g standard deviations from the mean whiie Swift shoes are - standard deviations from the mean. C) Swift. Swift shoes are — 3-9-9 standard deviations from the mean while Endurarnax shoes are 59 - 1-5-0- standard deviations from the mean. 59 D) Swift. Swift shoes are — 35%?- standard deviations from the mean while Endurainax shoes are - %— standard deviations from the mean. E) Enduramax. Enduramax shoes are - lég— standard deviations from the mean while Swift 59 shoes are — wig)" standard deviations from the mean. 25) The mean weights for medium navel oranges is 9.8 ounces. Suppose that the standard deviation 25) for the oranges is 3.3 ounces. Which would be more iikeiy, an orange weighing 14 ounces or an orange weighing 4.9 ounces? Explain. A) A 14; ounce orange is more likely (z m 4.48) compared with an orange weighing 4.9 ounces (2 m 1.27). B) A 4.9 ounce orange is more likely (z = 1.27) compared with an orange weighing 14 ounces (z = 4.48). C) A 14 ounce orange is more likely (z z 1.27) compared with an orange weighing 4.9 ounces (2 = 4.48). D) A 4.9 ounce orange is more iikely (z = 4.48) compared with an orange weighing 14 ounces (2 = 1.27). E) A 4.9 ounce orange is more iikeiy (z r: 1.48) compared with an orange weighing 14 ounces (2 m 4.24). Pick the appropriate standard deviation. 26) You heard that the average number of years of Experience among stockbrokers is 15 years. You 26) can't remember the standard deviation. Find an appropriate standard deviation. A) 9 years B) 3 years C) 3 months D) 6 months E) 9 months 27) The average number of pounds of sugar a person eats per year is 5. Find an appropriate standard deviation. A) 10 pounds B) 0.1 pounds C) 1 pound D) 4 pounds E) 5 pounds 28) The average weight of a newborn infant is 6.6 pounds. Fahd an appropriate standard deviation. A) 0.3 pound B) 1 pound C) 6 pounds D) 0.1 pound E) 3 pounds 29) The average score on the Chapter 4 mathematics test was 60 points (out of 100 points). Find an appropriate Standard deviation. A) 1 point B) 3 points C) 20 points D) 8 points E) 16 points 30) A salesman‘s commission averages $15,300 per year. Find an appropriate standard. deviation. A) $15,000 B) $500 C) $1000 D) $10,000 E) $4000 Draw the Normal model and use the 68.95—99.57 Rule to answer the question. 31) The systolic blood pressure of 18~year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. Draw and labei the Normal model for systoiic blood pressure. What percentage of18—year—old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg? A) 84 96 108 120 132 144 156 Blood Pressure (mm Hg) :99.7% B} 84 96 108 120 132 144 156 Blood Pressure (mm Hg) ; 68% 2’7) 28) 29) 30) 31) C) 84 96 108 120 132 144 156 Blood Pressure (mm Hg) ,' 95% 13) 84‘: 96 108 120 132. 144 156 Blood Pressure (mm Hg) ; 34% E) 84 96 108 120 132 144 156 Blood Pressure (mm Hg) ; 84% 32) An Engfish instructor gave a final exam and found a mean score of 68 points and a standard 32) deviation of 5.5 points. Assume that a Normal model can be applied. Draw and label the Normal model for the exam scores. Then find the intervai for the central 68% of the scores. A) 46 51.5 62.5 68 73.5 84.5 90 Exam Score ;62.5 to 73.5 points 13} 57 62.5 68 73.5 79 84.5 90 Exam Score ; 68 to 79 points If} C) 51.5 57 62.5 68 73.5 79 84.5 Exam Score ; 57 to 79 points D) 4.6 51.5 57 62.5 68 73.5 79 Exam Score ; 57 to 68 points E) 51.5 57 62.5 68 73.5 79 84.5 Exam Score ; 62.5 to 73.5 points 33) An English instructor gave a final exam and found a mean score 0f65 points and a standard 33) deviation of 6.3 points. Assume that a Normal model can be applied. Draw and label the Normal model for the exam scores. What percent of scores should be between77.6 and 83.9 points? A) 46.1 52.4 58.7 65 71.3 77.6 83.9 Exam Score ;4.'7% 3) 46.1 52.4 58.7 65 71.3 77.6 83.9 Exam Score ;5% ll C) 46.1 52.4 58.7 65 71.3 77.6 83.9 Exam Score ;2.35% D) 46.1 52.4 58.7 65 71.3 77.6 83.9 Exam Score ,' 34.6206349% E) 46.1 52.4 58.7 65 71.3 77.6 83.9 Exam Score ; 2.5% 34) Assuming a Normal model applies, a. tawn's average annual snowfall (in inches) is modeled by 34) N(45, 9). Draw and label the Normal model. Then find the interval for the middle 95% of snowfall. A) 18 27 36 45 54 63 72 Snowfall (in) ;27 to 63 13) 9 18 27 36 45 54 63 Snowfall (in) ; 18 to 54 12 C) 27 36 45 54 63 72 81 SnowfaH (in) ;36 to 72 D) 18 27 36 45 54 63 72 Snowfall (in) ; 36 to 54 E) 9 18 36 45 54 '72 81 SnowfaH (in) ; 18 to 72 35) Assuming a Normal mode} applies, a town's average annual snowfall (in inches) is modeled by 35) N016, 2). Draw and label the Normal model. What percent of snowfall is between 40 inches and 42 inches? A) 40 42 44 46 48 50 52 Snowfall (in) ,' 5% 13) 4:0 42 44 46 48 50 52 Snowfail (in) ; 2.2% 13 C) 40 42.44 46 48 50 52 Snowfall (in) ;2.35% D) 40 42 44 46 48 50 52 Snowfall (in) ;2.5% E) 4:0 42 44 46 48 50 52 Snowfall (in) ; 4.7% Solve the problem. 36) The volumes of soda in quart soda bottles can be described by a Normal model with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles can we expect to have a volume less than 32 oz? A) 40.13% B) 9.87% C) 38.21% D) 47.15% E) 59.87% 37) The lengths of human pregnancies can be described by a Normal model with a mean of 268 days and a standard deviation of 15 days. What percentage can we expect for a pregnancy that Will last at least 300 days? A) 98.34% B) 1.79% C) 1.66% D) 1.99% E) 48.34% ‘ 38) The test scores from a recent Mathematics test are as follows: 95.5, 65.9, 93.2, 88.6, 56.8, 50, 86.4, 54.5, 40.9, 77.3, 79.5, 65.9, 70.5, 77.3, 81.8, 50, 79.5, and 68.2. The mean score was 71.2 with a standard deviation of 15.5. If the Normal model is appropriate, What percent of the scores will be less than 40.2? A) 10% B) 16% C) 0.15% D) 2.5% a) 5% 39) A town’s average snowfall is 43 inches per year with a standard deviation of 8 inches. According to the Normal model, what percent of snowfall is less than 3 standard deviations from the mean? A) 16% B) 0.15% C) 5% o) 0.3% s) 2.5% 14 36) 37) 38) 39) 40) For a recent English exam, use the Normal model N(73, 9.2) to find the percent of scores under 58. 40) Round to the nearest tenth of a percent. A) 94.8% B) 95.8% C) 4.2% D) 5.2% E) 1.63% 41) Descriptive Statistics 41) Varable N Mean Median TrMean StDev SE Mean score 50 1045.7 1024.7 1041.9 221.9 31.4 Varable Minimum Maximum Q1 Q3 score 628.9 1577.1 877.7 1219.5 Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z = —1.2. What score did this student receive on the test? A) 1083.38 8) 1008.02 C) 266.28 D) 779.42 E) 1311.98 Find the percent of a standard Normal model found in the given region. Bound to the nearest hundredth of a percent 42) 0 < z < 3.01 42) A) 99.87% B) 50.13% C) 43.67% D) 12.17% E) 49.87% 4.3) 2: < 1.13 43) A) 89.07% B) 87.08% C) 12.92% D) 84.85% E) 88.09% 44) 0.7 < z < 1.98 44) A) 23.45% B) 21.81% C) 173.41% D) "«21.81% E) 21.75% 45) z > $1.82 45) A) 6.44% B) 3.44% C) 92.57% D) 96.56% E) 46.56% 46) z.< 0.97 46) A) 83.15% B) 83.40% C) 16.60% D) 82.35% E) 80.78% In a standard Normal model, state what value(s) of 25 cuts off the described region. 47) the lowest 96% 47) A) 1.75 B)1.03 C) —1.38 D) -1.75 E) 1.82 48) the lowest 9% 48) A) ~1.26 B) 1.34 C) 4.34 D) 4.45 E) —1.39 49) the highest 7% 49) A) 1.48 B) 1.26 C) —1.48 D) 1.39 E) 1.45 15 50) the highest 86% A) —1.02 B) 1.08 C) 0.8051 D) «4.08 E) 0.5557 51) the middle 96% A) -205 to 2.05 8) —3.00 to 8.00 C) 0 to 2.05 D) 4.75 to 1.75 E) —2.33 to 2.83 Solve the problem. Round to the nearest tenth. 52) For a recent English exam, use the Normal model N(73, 9.2) to find the score that represents the 30th percentile. A) 61.2 B) 63.8 C) 77.8 D) 82.2 E) 68.2 53) For a recent English exam, use the Normal model N03, 9.2) to find the score that represents the 60th percentile. A) 63.8 B) 70.7 C) 48.8 D) 82.2 E) 75.3 54) Based on the Normal model for snowfall in a certain town N{57, 8), how many inches of snow would IePIESent the 75th percentile? A) 51.6 inches B) 62.4 inches C) 65 inches D) 42.8 inches E) 49 inches 55) Based on the Normal model for car speeds on an old town highway NW7, 9.1), what is the cutoff value for the highest 15% of the speeds? A) about 86.5 mph B) about 65.5 mph C) about 67.5 mph D) about 11.6 mph E) about 63.1 mph 16 50) 51) 52) 53) 54) 55) 56) Based on the Normal model for car speeds on an old town highway N(77, 9.1), What are the cutofl values for the middle 20% of the speeds? A) about 95.2 mph, about 58.8 mph 13) about 61.6 mph, about 92.4 mph C) about 86.1 mph, about 67.9 mph D) about 74.7 mph, about 79.3 mph E) about 84.7 mph, about 69.3 mph Find the missing parameter. 57) p r: 60.0, 4.01% below 53; o 2: ? A)1.S8 B) 4.0 C) 8.0 D) 3.87 E) 2.0 58) U m 0.01, 2.28% below 0.32; p :2 ? A) 0.25 B) 0.55 C) 0.60 D) 0.34 E) 1.30 59) p = 30, 37% below 20; o‘ = ? A) 3.03 B) —0.33 C) 7.4 D) 0.37 E) 30.3 60) p z 0.38, 20% above 0.50; o = ? A) 0.143 B) 0.84 C) 0.20 D) 1.43 E) 0.1 61) o x 16, 20% below 100; p m ? A) “0.2 B) m0.84 C) 113.44 D) 0.2 E) 11.34 Soive the problem. Round to the nearest hundredth. 62) After increased patrol, cars on an old town highway travel at speeds averaging 53 mph. If 93% of vehicles travel below 68 mph, What approximate standard deviation could represent this model (assuming a Normal model is appropriate)? A) 31.76 B) 49.29 C) 40.14 D) 10.14 E) 63.24 63) After increased patrol, 33% of vehicles on an old town highway travel below 45 mph with a standard deviation of 5.8. Assuming a Normal model is appropriate, find the mean speed. A) 50.8 mph B) 47.55 mph C) 42-45 mph D) 14.85 mph E) 1.91 mph 17 56) 57) 58) 59) 60) 61) 62) 63) 64) On a recent English exam, scores averaged 79 points. if 41% of scores fell below '70 points, find an approximate standard deviation (assuming the Normal model is appropriate). A) 28.7 B) “91.30 C) w64:7.83 D) 32.39 E) 39.13 65) On a recent English exam, if 20% of scores fell below 60 points and the standard deviation is 6.0, find the mean score (assuming the Normal model is appropriate). A) —-54.~.96 B) 65.04 C) 12 D) 1.20 E) 66 Solve the problem. 66) The scores for a recent English exam can be represented by the Normal model N{66, 7.4). What score would you expect to be unusually low for this exam? A) 73.4. B) 58.6 C) 43.8 D) 62.3 s) 88.2 6’?) The annual snowfall in a town can be represented by the Normal model NGM, 7.3). What amount of snowfall would you expect to be unusuaiiy low for this town? A) 36.7 inches B) 65.9 inches C) 40.35 inches D) 51.3 inches E) 22.1 inches 68) Here are some scores from a recent Mathematics exam: 95.5, 65.9, 93.2, 80.6, 56.8, 50, 86.4, 54.5, 40.9, 77.3, 79.5, 10, 65.9, 70.5, 15, 77.3, 81.8, 12, 50, 79.5, 60.2. Which is a better summary of the scores, the mean or the median? Explain. A) Mean, the data is so skewed to the right B) Mean, the data is so skewed to the left C) Median, the data is so skewed to the left D) Median, the data is so skewed to the right E) Either, the data is symmetric 69) Here are the weekly winnings for several local poker players: $100, $50, $125, $75, $80, $60, $110, $150, $300, $700, $115, $75, $1000, $5000. Which is a better summary of the spread, the standard deviation or the IQR? Explain. A) IQR, the distribution is symmetric B) SD, the distribution is skewed C) iQR, the distribution is skewed D) Either, the distribution is symmetric E) SD, the distribution is symmetric 18 64) 65) 66) 67) 68) 69) Provide an appropriate response. 70) Which of the following variables would most likely follow a Normal model? 70) A) weights of adult male elephants B) family income C) heights of singers in a cowed choir D) scores on an easy test E) all of these SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question '71) A local plumber makes house ealis. She charges $30 to corne out to the house and $40 per 71) hour for her services. to: example, a tip-hour service call costs $30 + $40M) = $190. The table shows summary statistics for the past month. Fill in the table to find out the cost of the service calls. Hours of Service Call Cost of Service Call 72) Costs for standard veterinary services at a local animal hospital follow a Normal model 72) with a mean of $80 and a standard deviation of $20. Draw and clearly label this model. 73) Costs for standard veterinary services at a local animal hospital follow a Normal model 73) with a mean of $80 and a standard deviation of $20. What is the IQR for the costs of standard veterinary services? Show your work. '74) A machine that fills cans with soda fills according to a Normal model with mean 12.1 ’74) ounces and standard deviation 0.05 ounces. Management wants to ensure that only 1% of cans are under—filled. if the mean fill of the cans remains at 12.1 ounces, What standard deviation does the filling machine need to have to achieve this goal? 19 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 75) The SPCA coilects the foliowing data about the dogs they house. Which of those variables about 75) German Shepherds is most likely to be described by a Normal model? A) weight 13) breed C) age D) veterinary costs E) number of days housed 76) Suppose that a Normal model describes fuel economy (miles per gallon) for automobiles and that a 76) Saturn has a standardized score (La—score) of +2.2. This means that Saturns... A) have a standard deviation of 2.2 mpg. B) get 2.2 mpg more than the average car. C) achieve fuel economy that is 2.2 standard deviations better than the average car. D) get 2.2 miles per gallon. E) get 2.2 times the gas mileage of the average car. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question) 77) A publishing company pays its Sales staff $600 a week plus a commission of $0.50 per 77) book sold. For example, a salesman who sold 4&0 books earned 600 + 0.500340) 2 $820.The newest employee had a pretty good week. Among all the salespeople her pay corresponded to a zwscore of +1.80. What was the zwscore of the number of books she sold? 78) Owners of an exercise gym believe that a Normal model is useful in projecting the number 78) of clients who wiil exercise in their gym each week. They use a mean of 800 clients and a standard deviation of 90 clients. What is the first quartile of the weekly number of clients? [Show work] 79) A roadway construction process uses a machine that pours concrete onto the roadway and 79) measures the thickness of the concrete so the roadway will measure up to the required depth in inches. "the concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if the roadway is thinner than the minimum 23 inch thickness, the company sets the machine to average 26 inches for the batches of concrete. They believe the thickness ievei of the machine's concrete output can be described by a Normal mode} with standard deviation 1.75 inches, What percent of the concrete roadway is under the minimum depth?{Show work} 20 80) A roadway construction process uses a machine that pours concrete onto the roadway and 80) measures the thickness of the concrete so the roadway will measure up to the required depth in inches. The concrete thickness needs to be consistent across the road, but the machine isn't perfect and it is costly to operate. Since there's a safety hazard if the roadway is thinner than the minimum 23 inch thickness, the company sets the machine to average 26 inches for the batches of concrete. They believe the thickness level of the machine's concrete output can be described by a Normal model with standard deviation 1.75 inches. Explain what achieving a smaller standard deviation means in this context. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 81) Suppose that a Normal model describes the acidity (pH) of rainwater, and that water tested after 81) last week's storm had a z—score of 1.8. This means that the acidity of that rain... A) had a pH 1.8 times that of average rainwater. 3) had a pH 1.8 higher than average rainfall. C) had a pH of 1.8. D) had a pit 1.8 standard deviations higher than that of average rainwater. E) varied with a standard deviation of 1.8 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 82) You learn that your company is sending you and several other employees to staff a new 82) office in China. While there everyone will earn the equivalent of their current salary, converted to Chinese currency at the rate of 8 yuans per dollar. In addition, everyone will earn a weekly foreign living allowance of 200 yuans. For example, since you are earning $1000 per week, your weekly salary in China will be 1000(8) + 200 = 8200 yuans. Among this group of employees going to China, your US salary has a zwscore of +1.20. What will your new z—score be, based on everyone's China salary? 83) A manufacturer claims that lifespans for their copy machines (in months) can be described 83) by a Normal model N(42,7). A company with a several large office buildings buys 200 of these copiers. The salesman tells the boss "190 (95%) of your new copiers will last between and m months." Comment on this claim. 84) A manufacturer claims that lifespans for their copy machines (in months) can be described 84) by a Normal model N(42,7). What percent of the copiers are expected to fail before 36 months? 85) A manufacturer claims that lifespans for their copy machines (in months) can be described 85) by a Normal model N(42,7). A competing manufacturer says that not only will 90% of their copiers last at least 36 months, 65% will last at least 42 months. What Normal model parameters is that manufacturer claiming? Show your work. 18(er mm) 21 Answer Key Testname: CHAPTER 6 THE STANDARD DEVIATION AS A RULER AND THRE NORMAL MODEL (REVIEW) 1) A 2) D 3) E 4) D 5) E 6) E 7) E 3) E 9) C 10) c: 11) c 12) c 13) B 14) D 15) B 16) D 17) c 13) A 19) c 20) 3 21) C 22) D 23) A 24) C 25) C 26) 3 27) c: 23) 13 29) D 30) E 31) C 32) E 33) c 34) A 35) c: 36) A 37) c 38) D 39) B 40) D 41) D 42) E 43) B 44) B 45) D 46) B 47) A 48) c 49) A 22 Answer Key Testname: CHAPTER 6 THE STANDARD DEVIATION As A RULER AND THRE NORMAL MODEL (REVIEW) 50) D 51) A 52) E 53) E 54) B 55) A 56) D 57) B 58) D 59) E 60) A 61) C 62) D 63) B 64) E 65) B 66) C 67) E 68) C 69) C 70) A 71) Statistic Hours of Service Call Cost of Service Call 72) Vet Bills 6) 20 40 00 80 19!! 120 14') “WW-— 99.7% 73) Q1 has 2 6 ~06? and Q3 has z 6 +0.67, so "067 a 139 6:. y z 00 m 067(20) = 66.6 and +0.67 = Jig—(€51 22> y a 80 + O.67(20) = 93.4. The IQR 6 Q3 ~— Q1 2 93.4 m 66.6 6 $26.80 23 Answer Key Testname: CHAPTER 6 THE STANDARD DEVIATION AS A RULER AND THRE NORMAL MODEL (REVIEW) ‘74) A zmscore of ~2.33 has 1% to its left, meaning that 1% of the cans would be undei—filled. 12 — 12.1 _ will __ 0 043 h :———— “2, z“, _ 233 O x: 335 01 we alas The standard deviation would need to be 0.043 ounces. 75) A 7’6) C 77) +1.80 78) Q1 => P a 0.25 and z x - 0.674, x —— 800 ~06? : 4 90 w60.66 = x ~— 800 x = 739.34 30 the first quartile is at 740 clients. 79) The concrete roadway is under minimum depth when less then 23 inches in thickness. z = 2:: 6 w ~17 2:» P a 0.043, 50 the model suggests about 4.3% is under the minimum depth. 80) A smaller standard deviation means that the thickness of the concrete will be more consistent. 81) D 82) +1.20 83) 28, 56. The claim is probably false. This model should provide a useful estimate of What might happen, but is not certain to predict What actually will happen 84) 19.6% 85) For 36 months 2 m “1.28 and for 42 months z = w0.385. Thus the difference of 6 months is 1.28 ~ 0.385 2 0.895 standard deviations. The model is N(44.6, 6.7) 24 ...
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This note was uploaded on 11/10/2009 for the course CAL 3452 taught by Professor Mr.sun during the Spring '09 term at Sungkyunkwan.

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Chapter 6 Review Problems - Chapter 6 The Standard...

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