Deck 5: The Standard Deviation As a Ruler and the Normal Model

Question 1

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 66,median = 80.2,range = 79,IQR = 58,Q1 = 26,standard deviation = 8.3.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: 35.65,mean: 75.9,median: 92.23,range: 90.85,IQR: 66.7,Q1: 22.1,SD: 9.545
B)Lowest score: 26.35,mean: 56.1,median: 68.17,range: 79,IQR: 49.3,Q1: 22.1,SD: 7.055
C)Lowest score: 26.35,mean: 56.1,median: 68.17,range: 67.15,IQR: 49.3,Q1: 22.1,SD: 7.055
D)Lowest score: 4.65,mean: 9.9,median: 12.03,range: 11.85,IQR: 8.7,Q1: 22.1,SD: 1.245
E)Lowest score: 26.35,mean: 56.1,median: 68.17,range: 79,IQR: 58,Q1: 22.1,SD: 7.055

Answer 1

Lowest score: 26.35,mean: 56.1,median: 68.17,range: 67.15,IQR: 49.3,Q1: 22.1,SD: 7.055

Question 2

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 131 minutes,mean = 77 minutes,median = 77 minutes,range = 101 minutes,IQR = 58,Q1 = 31,standard deviation = 15 minutes.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the left,mean higher than median.
B)Skewed to the right,mean lower than median.
C)Symmetric,mean same as median.
D)Skewed to the left,mean lower than median.
E)Skewed to the right,mean higher than median.

Answer 2

Symmetric,mean same as median.

Question 3

Here are some statistics for the annual Wildcat golf tournament: lowest score = 56,mean score = 90,median = 98,range = 94,IQR = 106,Q1 = 36,standard deviation = 11.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the left,mean higher than median.
B)Skewed to the left,mean lower than median.
C)Symmetric,mean lower than median.
D)Skewed to the right,mean higher than median.
E)Skewed to the right,mean lower than median.

Answer 3

Skewed to the left,mean lower than median.

Question 4

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 129 minutes,mean = 79 minutes,median = 79 minutes,range = 99 minutes,IQR = 64,Q1 = 32,standard deviation = 11 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: 6.32 minutes,SD: 0.88 minutes
B)Mean: 85.32 minutes,SD: 11 minutes
C)Mean: 85.32 minutes,SD: 11.88 minutes
D)Mean: 72.68 minutes,SD: 10.12 minutes
E)Mean: 72.68 minutes,SD: 11 minutes

Question 5

The freethrow percentages for the participants in a basketball tournament were compiled.The percents ranged from 33% to 99% with a mean of 56% and a standard deviation of 7%.The quartiles and median percentages were 43%,87%,and 56%.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the left,mean higher than median.
B)Skewed to the right,mean higher than median.
C)Skewed to the left,mean lower than median.
D)Skewed to the right,mean lower than median.
E)Symmetric,mean same as median.

Question 6

Here are some summary statistics for the recent English exam: lowest score = 36,mean score = 71,median = 85.2,range = 74,IQR = 61,Q1 = 28,standard deviation = 8.3.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the right,mean higher than median.
B)Symmetric,mean lower than median.
C)Skewed to the left,mean lower than median.
D)Skewed to the right,mean lower than median.
E)Skewed to the left,mean higher than median.

Question 7

Here are some summary statistics for last years basketball team scoring output: lowest score = 18 points,mean = 58 points,median = 52 points,range = 97 points,IQR = 46,Q1 = 23,standard
Deviation = 9 points.Suppose the opponents' scoring output was 10% lower.Find the opponents' mean and standard deviation.

A)Mean: 52.2 points,SD: 8.1 points
B)Mean: 52.2 points,SD: 9 points
C)Mean: 63.8 points,SD: 9.9 points
D)Mean: 63.8 points,SD: 9 points
E)Mean: 5.8 points,SD: 0.9 points

Question 8

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $60,000,mean salary = $140,000,median = $100,000,range = $240,000,IQR = $120,000,first quartile = $70,000,standard deviation = $80,000.
Suppose that business has been good and the company gives every employee a $10,000 raise.Give the new value of each of the summary statistics.

A)Minimum: 60,000;Mean: 140,000;Median: 100,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
B)Minimum: 70,000;Mean: 150,000;Median: 100,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
C)Minimum: 70,000;Mean: 140,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
D)Minimum: 70,000;Mean: 150,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000
E)Minimum: 60,000;Mean: 150,000;Median: 110,000;Range: 240,000;
IQR: 120,000;Q1: 80,000;SD: 80,000

Question 9

Here are some summary statistics for the size of forest fires last year: smallest fire = 74 acres,mean = 451 acres,median = 451 acres,range = 7,926 acres,IQR = 387,Q1 = 180,standard deviation = 61 acres.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the right,mean higher than median.
B)Symmetric,mean same as median.
C)Skewed to the left,mean higher than median.
D)Skewed to the right,mean lower than median.
E)Skewed to the left,mean lower than median.

Question 10

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 19 cm,mean = 40 cm,median = 33 cm,range = 81 cm,IQR = 45 cm,Q1 = 16 cm,standard deviation = 11 cm.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the left,mean higher than median.
B)Skewed to the right,mean higher than median.
C)Skewed to the left,mean lower than median.
D)Skewed to the right,mean lower than median.
E)Symmetric,mean higher than median.

Question 11

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 95,median = 103,range = 92,IQR = 110,Q1 = 38,standard deviation = 15.Suppose it was very windy and all the golfers' scores went up by 7 strokes.Tell the new value for each of the summary statistics.

A)Lowest score: 65,mean: 102,median: 110,range: 92,IQR: 110,Q1: 45,SD: 15
B)Lowest score: 65,mean: 102,median: 110,range: 85,IQR: 110,Q1: 45,SD: 15
C)Lowest score: 65,mean: 102,median: 110,range: 85,IQR: 117,Q1: 45,SD: 15
D)Lowest score: 65,mean: 95,median: 103,range: 85,IQR: 110,Q1: 45,SD: 15
E)Lowest score: 65,mean: 102,median: 110,range: 85,IQR: 110,Q1: 45,SD: 22

Question 12

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 50 km/h to 65 km/h with a mean speed of 55 km/h and a standard deviation of 7 km/h.The quartiles and median speeds were 53 km/h,62 km/h,and 52 km/h.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 right,mean higher than median.
C)Skewed to the left,mean higher than median.
D)Skewed to the left,mean lower than median.
E)Symmetric,mean higher than median.

Question 13

Here are some summary statistics for last years basketball team scoring output: lowest score = 19 points,mean = 55 points,median = 49 points,range = 96 points,IQR = 52,Q1 = 22,standard deviation = 6 points.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Symmetric,mean higher than median.
B)Skewed to the left,mean higher than median.
C)Skewed to the right,mean higher than median.
D)Skewed to the right,mean lower than median.
E)Skewed to the left,mean lower than median.

Question 14

Here are some summary statistics for the size of forest fires last year: smallest fire = 92 acres,mean = 462 acres,median = 462 acres,range = 7,908 acres,IQR = 375,Q1 = 185,standard deviation = 57 acres.If it costs $1200 per acre to fight the fires,find the minimum,median,standard deviation,and IQR of the cost.

A)Minimum: 1,292,median: 1,662,SD: 1,257,IQR: 1,575
B)Minimum: 92,median: 462,SD: 57,IQR: 375
C)Minimum: 110,400,median: 554,400,SD: 68,400,IQR: 450,000
D)Minimum: 110,400,median: 462,SD: 68,400,IQR: 375
E)Minimum: 110,400,median: 554,400,SD: 57,IQR: 375

Question 15

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $30,000,mean salary = $70,000,median = $50,000,range = $120,000,IQR = $60,000,first quartile = $35,000,standard deviation = $40,000.
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)Skewed to the left;mean is lower than median.
C)Symmetric,mean is higher than median.
D)Skewed to the left,mean is higher than median.
E)Skewed to the right,mean is lower than median.

Question 16

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 137 grams to 196 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 151,249,and 202 grams.Is the distribution symmetric,skewed to the left,or skewed to the right? Explain.

A)Skewed to the left,mean higher than median.
B)Skewed to the right,mean higher than median.
C)Skewed to the right,mean lower than median.
D)Skewed to the left,mean lower than median.
E)Symmetric,mean lower than median.

Question 17

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 19 cm,mean = 47 cm,median = 40 cm,range = 81 cm,IQR = 54,Q1 = 19,standard deviation = 10 cm.Suppose snowfall was tracked for 5 additional years and the annual snowfall was found to increase by 20%.Find the new mean and standard deviation.

A)Mean: 9.4 cm,SD: 2 cm
B)Mean: 37.6 cm,SD: 10 cm
C)Mean: 56.4 cm,SD: 10 cm
D)Mean: 37.6 cm,SD: 8 cm
E)Mean: 56.4 cm,SD: 12 cm

Question 18

The speed vehicles traveled on a local road was recorded for one month.The speeds ranged from 48 km/h to 63 km/h with a mean speed of 57 km/h and a standard deviation of 6 km/h.The quartiles and median speeds were 51 km/h,60 km/h,and 54 km/h.Suppose increased patrols reduced speeds by 7%.Find the new mean and standard deviation.Express your answer in exact decimals.

A)Mean: 53.01 km/h,SD: 5.58 km/h
B)Mean: 53.01 km/h,SD: 6 km/h
C)Mean: 60.99 km/h,SD: 6.42 km/h
D)Mean: 3.99 km/h,SD: 0.42 km/h
E)Mean: 60.99 km/h,SD: 6 km/h

Question 19

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 305 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 148,246,and 202 grams.Find the range and IQR of the weights.

A)Range: 41 grams,IQR: 53 grams
B)Range: 98 grams,IQR: 165 grams
C)Range: 445 grams,IQR: 98 grams
D)Range: 41 grams,IQR: 165 grams
E)Range: 165 grams,IQR: 98 grams

Question 20

The freethrow percentages for the participants of a basketball tournament were compiled.The percents ranged from 40% to 96% with a mean of 53% and a standard deviation of 8%.The quartiles and median percentages were 50%,84%,and 53%.This year's tournament percentages are 3% higher than last year's tournament percentages.Find last year's tournament mean,median,and standard deviation of the freethrow percentages.

A)Mean: 56%,median: 56%,SD: 11%
B)Mean: 53%,median: 56%,SD: 11%
C)Mean: 51.5%,median: 53%,SD: 7.8%
D)Mean: 51.5%,median: 54.4%,SD: 7.8%
E)Mean: 50%,median: 50%,SD: 5%

Question 21

The speed vehicles travelled on a local road was recorded for one month.The speeds ranged from 46 km/h to 61 km/h with a mean speed of 56 km/h and a standard deviation of 8 km/h.The quartiles and median speeds were 49 km/h,58 km/h,and 53 km/h.Suppose during the month,one driver was clocked at 25 km/h.Which of the summary statistics might not change if that data value was added to the distribution?

A)Mean,IQR
B)Median,IQR
C)Range,SD
D)Median,range
E)Q1,Q3

Question 22

Here are the summary statistics for the monthly payroll for an accounting firm: lowest salary = $15,000,mean salary = $35,000,median = $25,000,range = $60,000,IQR = $30,000,first quartile = $17,500,standard deviation = $20,000.
Between what two values are the middle 50% of the salaries found?

A)$15,000 and $75,000
B)$17,500 and $37,500
C)$17,500 and $30,000
D)$35,000 and $25,000
E)$17,500 and $47,500

Question 23

A town's average snowfall is 40 cm per year with a standard deviation of 12 cm.How many standard deviations from the mean is a snowfall of 64 cm?

A)0.44 standard deviations below the mean
B)2.00 standard deviations above the mean
C)2.00 standard deviations below the mean
D)1.60 standard deviations above the mean
E)0.44 standard deviations above the mean

Question 24

The freethrow percentages for the participants of a basketball tournament were compiled.The percents ranged from 39% to 99% with a mean of 50% and a standard deviation of 5%.The quartiles and median percentages were 49%,87%,and 50%.Suppose one participant did not make any of his attempted freethrows (0%).Which of the summary statistics might not change if that data value was added to the distribution?

A)Q1,Q3
B)Mean,IQR
C)Median,IQR
D)Range,SD
E)Median,range

Question 25

The average number of average number of hours per day a university student spends on homework is 5 hours with a standard deviation of 1.25 hours.How many standard deviations from the mean is 2 hours spent on homework?

A)2.40 standard deviations below the mean
B)1.20 standard deviations below the mean
C)2.50 standard deviations above the mean
D)1.20 standard deviations above the mean
E)2.40 standard deviations above the mean

Question 26

Mario's poker winnings average $319 per week with a standard deviation of $56.How many standard deviations from the mean is winning $195?

A)About 1.11 standard deviations below the mean
B)About 2.21 standard deviations above the mean
C)About 1.64 standard deviations below the mean
D)About 2.21 standard deviations below the mean
E)About 1.11 standard deviations above the mean

Question 27

Here are some summary statistics for the size of forest fires last year: smallest fire = 72 acres,mean = 493 acres,median = 493 acres,range = 7,928 acres,IQR = 370,Q1 = 197,standard deviation = 59 acres.Between what two values are the middle 50% of fire sizes found?

A)123.25 and 369.75
B)98.6 and 394.4
C)197 and 567
D)72 and 8000
E)246.5 and 493

Question 28

Here are some summary statistics for the recent English exam: lowest score = 31,mean score = 67,median = 81.2,range = 79,IQR = 60,Q1 = 27,standard deviation = 8.6.Between what two values are the middle 50% of the scores found?

A)31 and 110
B)67 and 81.2
C)27 and 87
D)16.75 and 50.25
E)20.3 and 60.9

Question 29

The setter on your school's volleyball team average 58 assists per match with a standard deviation of 6.How many standard deviations from the mean is an outing with 79 assists?

A)1.75 standard deviations below the mean
B)1.36 standard deviations below the mean
C)3.50 standard deviations below the mean
D)3.50 standard deviations above the mean
E)1.75 standard deviations above the mean

Question 30

A local ice cream shop hand scoops each of its ice cream cones.The cones vary in weight from 140 grams to 207 grams with a mean of 181 grams and a standard deviation of 34 grams.The quartiles and median weights are 154,252,and 202 grams.A customer makes a special order of a 16 ounce cone.Which of the summary statistics might not change if that data value was added to the distribution?

A)Range,SD
B)Median,IQR
C)Median,range
D)Mean,IQR
E)Q1,Q3

Question 31

Here are some statistics for the annual Wildcat golf tournament: lowest score = 58,mean score = 97,median = 105,range = 92,IQR = 105,Q1 = 39,standard deviation = 16.Between what two values are the middle 50% of the scores found?

A)26.25 and 78.75
B)58 and 150
C)39 and 144
D)24.25 and 67.9
E)97 and 105

Question 32

Here are some summary statistics for annual snowfall in a certain town compiled over the last 15 years: lowest amount = 18 cm,mean = 49 cm,median = 42 cm,range = 82 cm,IQR = 50,Q1 = 20,standard deviation = 10 cm.Between what two values are the middle 50% of snowfall found?

A)20 and 70
B)12.25 and 36.75
C)49 and 42
D)10.5 and 31.5
E)18 and 100

Question 33

Here are some summary statistics for all of the runners in a local 12 kilometre race: slowest time = 132 minutes,mean = 76 minutes,median = 76 minutes,range = 102 minutes,IQR = 62,Q1 = 30,standard deviation = 10 minutes.Between what two values are the middle 50% of times?

A)15.2 and 60.8
B)132 and 30
C)19 and 57
D)38 and 76
E)30 and 92

Question 34

Here are some summary statistics for last year's basketball team scoring output: lowest score = 23 points,mean = 53 points,median = 47 points,range = 92 points,IQR = 51,Q1 = 32,standard deviation = 5 points.Between what two values are the middle 50% of scores found?

A)53 and 47
B)23 and 115
C)13.25 and 3,975
D)32 and 83
E)11.75 and 35.25

Question 35

The average size of forest fires last year was 968 acres with a standard deviation of 182 acres.How many standard deviations from the mean is a forest fire consuming 245 acres?

A)About 3.97 standard deviations below the mean
B)About 1.35 standard deviations above the mean
C)About 3.97 standard deviations above the mean
D)About 1.99 standard deviations below the mean
E)About 1.99 standard deviations above the mean

Question 36

The average number of babies born in a certain town each year is 218 with a standard deviation of 26.How many standard deviations from the mean is a year with 387 babies born?

A)3.25 standard deviations below the mean
B)6.50 standard deviations above the mean
C)3.25 standard deviations above the mean
D)6.50 standard deviations below the mean
E)1.78 standard deviations above the mean

Question 37

The average number of days absent per student per year at West Valley School is 16 days with a standard deviation of 5 days.How many standard deviations from the mean is of 6 absent days?

A)0.83 standard deviations above the mean
B)1.83 standard deviations below the mean
C)2.00 standard deviations above the mean
D)2.00 standard deviations below the mean
E)1.83 standard deviations above the mean

Question 38

Suppose that the average amount of sugar a person eats per year is 5 kg with a standard deviation of 1.7 kg.How many standard deviations from the mean is the consumption of 14 kg of sugar?

A)About 3.00 standard deviations above the mean
B)About 3.00 standard deviations below the mean
C)About 2.94 standard deviations above the mean
D)About 5.29 standard deviations above the mean
E)About 5.29 standard deviations below the mean

Question 39

The weights of children age two average 25 pounds with a standard deviation of 4 pounds.How many standard deviations from the mean is a weight of 15 pounds?

A)2.50 standard deviations below the mean
B)1.40 standard deviations above the mean
C)1.40 standard deviations below the mean
D)1.67 standard deviations above the mean
E)2.50 standard deviations above the mean

Question 40

The mean test score on a statistics test was 72 with a standard deviation of 10.How many standard deviations from the mean is a test score of 90?

A)1.80 standard deviations above the mean
B)1.80 standard deviations below the mean
C)0.69 standard deviations above the mean
D)0.80 standard deviations above the mean
E)0.69 standard deviations below the mean

Question 41

The average amount of sugar a person eats per year is 4 kg.A person who consumes 3.25 kg of sugar has a z-score of -0.75.Find the standard deviation.

A)4 kg
B)1 kg
C)0.1 kg
D)5 kg
E)10 kg

Question 42

You heard that the average number of years of experience among stockbrokers is 14 years.You can't remember the standard deviation somebody with 8 years experience has a z-score of -2.Find the standard deviation.

A)3 years
B)9 months
C)6 months
D)9 years
E)3 months

Question 43

A basketball coach kept statistics for his team in free throw percentage and steals (among others).At the last game,Erin's free throw percentage was 79% and she had 4 steals.The team averaged 90% from the free throw line with a standard deviation of 6% 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 -

Standard deviations from the mean while 79% free throw average is -

Standard deviations from the mean.
B)Free throw percentage.79% free throw average is -

Standard deviations from the mean while 4 steals is -

Standard deviations from the mean.
C)Free throw percentage.79% free throw average is -

Standard deviations from the mean while 4 steals is -

Standard deviations from the mean.
D)One can't compare the two categories,they are too different.
E)Steals.4 steals is -

Standard deviations from the mean while 79% free throw average is -

Standard deviations from the mean.

Question 44

Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for Swift shoes is 54 km and 124 km for Enduramax,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.

A)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
B)Enduramax.The Enduramax shoes have a longer mean shoe life.
C)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
D)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
E)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.

Question 45

A town's snowfall in December averages 10 cm with a standard deviation of 10 cm while in February,the average snowfall is 42 cm with a standard deviation of 16 cm.In which month is it more likely to snow 32 cm? Explain.

A)February.Snowfall of 32 cm is

From the mean while snowfall of 32 cm is -

From the mean in December.
B)December.Snowfall of 32 cm is -

From the mean while snowfall of 32 cm is

From the mean in February.
C)It is equally likely in either month.One can't predict Mother Nature.
D)December.Snowfall of 32 cm is

From the mean while snowfall of 32 cm is -

From the mean in February.
E)February.Snowfall of 32 cm is -

From the mean while snowfall of 32 cm is

From the mean in December.

Question 46

Adam played golf on Saturday and Sunday.He scored 82 both days.The scores of all golfers Saturday averaged 68 with a standard deviation of 17.The scores on Sunday averaged 81 with a standard deviation of 9.On which day did Adam do better compared with the other golfers? Explain.

A)Sunday.A score of 82 Sunday is

Standard deviations from the mean while a score of 82 Saturday is

Standard deviations from the mean.
B)Sunday.A score of 82 Sunday is

Standard deviations from the mean while a score of 82 Saturday is

Standard deviations from the mean.
C)Saturday.A score of 82 Saturday is

Standard deviations from the mean while a score of 82 Sunday is

Standard deviations from the mean.
D)He did not do better either day,he scored the same.
E)Saturday.A score of 82 Saturday is

Standard deviations from the mean while a score of 82 Sunday is

Standard deviations from the mean.

Question 47

The mean weight of babies born in a hospital last year was 2.84 kg.Suppose the standard deviation of the weights is 0.95 kg.Which would be more unusual,a baby weighing 1.8 kg or a baby weighing 3.83 kg? Explain.

A)A 1.8 kg baby is more unusual (z = -1.09)compared with a 3.83 kg baby (z = 1.04).
B)A 3.83 kg baby is more unusual (z = 1.90)compared with a 1.8 kg baby (z = 4.05).
C)A 3.83 kg baby is more unusual (z = -1.09)compared with a 1.8 kg baby (z = -1.09).
D)A 1.8 kg baby is more unusual (z = -1.05)compared with a 3.83 kg baby (z = -1.04).
E)A 3.83 kg baby is more unusual (z = 1.04)compared with a 1.8 kg baby (z = -1.09).

Question 48

The local basketball team averages 65% from the freethrow line.A player who makes 72.5% of his freethrows has a z-score of 1.5.Find the standard deviation.

A)5%
B)15%
C)3%
D)1%
E)10%

Question 49

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 label the Normal model for systolic blood pressure.What percentage of 18-year-old women have a systolic blood pressure between 96 mm Hg and 144 mm Hg?

A)

;95%
B)

;99.7%
C)

;68%
D)

;34%
E)

;84%

Question 50

The average attendance for your local hockey team is 450,000 per game.The attendance during the last game was only 320,000 which corresponded to a z-score of -16.25.Find the standard deviation.

A)1000 people
B)17,000 people
C)3000 people
D)20,000 people
E)8000 people

Question 51

The average score on a mathematics test was 64%.A student who scored 80% had a z-score of 2.Find the standard deviation.

A)16%
B)8%
C)3%
D)20%
E)1%

Question 52

A salesman's commission averages $23,700 per year.Last year his commission was $18,900 which corresponded to a z-score of -1.2.Find the standard deviation.

A)$10,000
B)$500
C)$15,000
D)$1000
E)$4000

Question 53

The average speed cars travel on a road is 77 km/h.A car travelling 60 km/h has a z-score of -1.7.Find the standard deviation.

A)40 km/h
B)10 km/h
C)30 km/h
D)0.5 km/h
E)1 km/h

Question 54

A family of four averages 85 loads of laundry per month.One such family does 62 loads per month and has a z-score of -2.3.Find the standard deviation.

A)20 loads
B)10 loads
C)1 load
D)2 loads
E)3 loads

Question 55

The amount of Jen's monthly phone bill is normally distributed with a mean of $55 and a standard deviation of $8.Draw and label the Normal model for Jen's monthly phone bill.In what interval would you expect the central 68% of bills to be found?

A)

;$31 to $79
B)

;$39 to $71
C)

;$47 to $71
D)

;$47 to $63
E)

;$39 to $63

Question 56

The mean weights for medium navel oranges is 274 grams.Suppose that the standard deviation for the oranges is 92 grams.Which would be more likely,an orange weighing 392 grams or an orange weighing 137 grams? Explain.

A)A 137 gram orange is more likely (z = 1.49)compared with an orange weighing 392 grams (z = 4.24).
B)A 137 gram orange is more likely (z = -1.49)compared with an orange weighing 392 grams (z = 1.28).
C)A 137 gram orange is more likely (z = 1.28)compared with an orange weighing 392 grams (z = -1.49).
D)A 392 gram orange is more likely (z = -1.49)compared with an orange weighing 137 grams (z = 1.28).
E)A 392 gram orange is more likely (z = 1.28)compared with an orange weighing 137 grams (z = -1.49).

Question 57

The average amount of snowfall in a certain town is 54 cm per year.Last year's snowfall was 67.5 cm which corresponded to a z-score of 1.5.Find the standard deviation.

A)5 cm
B)30 cm
C)9 cm
D)20 cm
E)1 cm

Question 58

The average weight of a newborn infant is 2.7 kg.An infant that ways 3.15 kg has a z-score of 1.Find the standard deviation.

A)0.05 kg
B)0.14 kg
C)1.35 kg
D)0.45 kg
E)2.7 kg

Question 59

An English instructor gave a final exam and found a mean score of 69 points and a standard deviation of 5.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the interval for the central 68% of the scores.

A)

;57.4 to 80.6 points
B)

;63.2 to 74.8 points
C)

;63.2 to 74.8 points
D)

;57.4 to 69 points
E)

;69 to 80.6 points

Question 60

Two different running shoe manufacturers market running shoes to first time marathon runners.Swift claims a mean shoe life of 600 km,while Enduramax claims a shoe life of 650 km.If the standard deviation for both shoes is 51 km,which shoe would you purchase before starting your marathon training (where you figure to run 500 km)? Explain.

A)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.
B)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
C)Swift.I only need to run 500 km and the Swift will last 100 km beyond that.
D)Enduramax.Enduramax shoes are -

Standard deviations from the mean while Swift shoes are -

Standard deviations from the mean.
E)Swift.Swift shoes are -

Standard deviations from the mean while Enduramax shoes are -

Standard deviations from the mean.

Question 61

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 greater than 86.7?

A)15.87%
B)0.15%
C)10%
D)34%
E)2.28%

Question 62

The volumes of soda in 1 litre cola bottle can be described by a Normal model with a mean of 0.95 L and a standard deviation of 0.04 L.What percentage of bottles can we expect to have a volume less than 0.94 L?

A)40.13%
B)9.87%
C)47.15%
D)38.21%
E)59.87%

Question 63

z < 1.13

A)89.07%
B)87.08%
C)12.92%
D)84.85%
E)88.09%

Question 64

An English instructor gave a final exam and found a mean score of 72 points and a standard deviation of 6.9 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 between 85.8 and 92.7 points?

A)

;5%
B)

;2.5%
C)

;2.35%
D)

;4.7%
E)

;35.9318841%

Question 65

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(50,6).Draw and label the Normal model.About what percent represents snowfall of less than 62 cm?

A)

;0.15%
B)

;2.5%
C)

;84%
D)

;99.85%
E)

;97.5%

Question 66

For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores over 85.Round to the nearest tenth of a percent.

A)88.5%
B)90.3%
C)9.7%
D)8.1%
E)11.5%

Question 67

0 < z < 3.01

A)99.87%
B)43.67%
C)49.87%
D)12.17%
E)50.13%

Question 68

An English instructor gave a final exam and found a mean score of 70 points and a standard deviation of 5.1 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Then find the percent of scores above 85.3 points.

A)

;0.3%
B)

;2.5%
C)

;16%
D)

;0.15%
E)

;5%

Question 69

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)1.66%
C)1.79%
D)48.34%
E)1.99%

Question 70

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(45,7).Draw and label the Normal model.What percent of snowfall is between 52 cm and 59 cm?

A)

;11%
B)

;13.5%
C)

;32%
D)

;16%
E)

;27%

Question 71

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(43,2).Draw and label the Normal model.What percent of snowfall is between 39 cm and 45 cm?

A)

;81.5%
B)

;41%
C)

;95%
D)

;68%
E)

;54.5%

Question 72

A town's average snowfall is 40 cm per year with a standard deviation of 5 cm.According to the Normal model,what percent of snowfall is less than 3 standard deviations from the mean?

A)15.87%
B)99.74%
C)5%
D)2.28%
E)0.26%

Question 73

A town's average snowfall is 45 cm per year with a standard deviation of 9 cm.Using a Normal model,what values should border the middle 68% of the model?

A)49.5 cm and 40.5 cm
B)45 cm and 41.94 cm
C)54 cm and 36 cm
D)63 cm and 27 cm
E)46.8 cm and 43.2 cm

Question 74

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)0.15%
B)10%
C)5%
D)15.87%
E)2.28%

Question 75

An English instructor gave a final exam and found a mean score of 70 points and a standard deviation of 6.8 points.Assume that a Normal model can be applied.Draw and label the Normal model for the exam scores.Describe the scores of the top 2.5%.

A)

;Higher than 90.4 points
B)

;Higher than 76.8 points
C)

;83.6 points
D)

;Higher than 83.6 points
E)

;Higher than 76.8 points

Question 76

A bank's loan officer rates applicants for credit.The ratings can be described by a Normal model with a mean of 200 and a standard deviation of 50.If an applicant is randomly selected,what percentage can be expected to be between 200 and 275?

A)6.68%
B)43.32%
C)93.32%
D)42.37%
E)5.00%

Question 77

Assuming a Normal model applies,a town's average annual snowfall (in cm)is modeled by N(42,8).Draw and label the Normal model.Then find the interval for the middle 95% of snowfall.

A)

;18 to 50
B)

;34 to 50
C)

;26 to 58
D)

;34 to 66
E)

;18 to 66

Question 78

For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores between 56 and 87.Round to the nearest tenth of a percent.

A)90.4%
B)3.2%
C)3.37%
D)9.7%
E)96.6%

Question 79

For a recent English exam,use the Normal model N(73,9.2)to find the percent of scores under 58.Round to the nearest tenth of a percent.

A)94.8%
B)4.2%
C)95.8%
D)1.63%
E)5.2%

Question 80

-2.41< z < 0

A)49.10%
B)9.48%
C)52.16%
D)50.80%
E)49.20%