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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 — 353— 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 — 399 standard deviations from the mean while Endurarnax shoes are 59  150 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~yearold 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....
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