Class 5: Standard Deviation 1) On a standardized test, scores range from 70 to 130. If the scores have a

normal distribution and the mean score is a 100, what is the standard

deviation?

.

2) Scores on a standardized test have a normal distribution. If the mean score

is 50 and the standard deviation is 5, what is the range from lowest to

highest possible scores?

A) 30 to 60

B) 35 to 65

C) 45 to 65

D) 45 to 55

E) 40 to 60

3) Scores on a standardized test have a normal distribution and range from 0

to 120 with a standard deviation of 20 points. What is the mean score on

the test?

A) 20

B) 30

C) 40

D) 60

E) 120

4) Scores on a standardized test have a normal distribution. If the mean score

is a 60 and 32 out of the 200 test takers score a 70 or above, what is the

standard deviation?

A) 10

B) 20

C) 32

D) 40

E) 50

5) Scores on a standardized test have a normal distribution. If 2% of the test

takers score below a 22, the sum of the scores of all test takers is 7,200,

and the mean score is 24, how many test takers score above a 25?

A) 6

B) 16

C) 32

D) 48

E) 300

6) In a college class, students’ heights range from 60 to 72 inches. If the

heights have a normal distribution and the mean height is 66 inches, what

is the standard deviation?

.

7) In an elementary school, students’ heights have a normal distribution. If the

mean height is 55 inches and the standard deviation is 1 inch, what is the

range from lowest to highest heights?

A) 50 to 58

B) 50 to 60

C) 48 to 60

D) 52 to 58

E) 52 to 60

8) In a middle school, students’ heights have a normal distribution and range

from 56 to 65 with a standard deviation of 1.5 inches. What is the mean

student height?

A) 57.5

B) 59

C) 60.5

D) 62

E) 63.5

9) In a high school, students’ heights have a normal distribution. If the mean

height is 67 inches and 48 out of the 300 test takers are below 62 inches

tall, what is the standard deviation?

A) 1.5

B) 2

C) 2.5

D) 3.5

E) 5

10) In a basketball league, players’ heights have a normal distribution. If 2%

of the players are above 84 inches tall, the sum of the players’ heights is

23,400 inches, and the mean height is 78 inches, how many players are

between 72 and 75 inches tall?

A) 36

B) 40

C) 42

D) 48

E) 50

11) Throughout the year, daily rainfall in Stumptown ranges from 0 to 12

centimeters. If the rainfall has a normal distribution and the mean total

rainfall is 6 centimeters, what is the standard deviation?

.

12) Total yearly rainfall in Angel City has a normal distribution. If the mean

yearly rainfall is 100 inches and the standard deviation is 5, what is the

range from lowest to highest yearly totals?

A) 90 to 110

B) 80 to 120

C) 85 to 115

D) 85 to 105

E) 90 to 120

13) Total yearly snowfall in Engine City has a normal distribution and ranges

from 26 to 38 inches with a standard deviation of 2 points. What is the

mean yearly snowfall in Engine City?

A) 28

B) 29

C) 30

D) 31

E) 32

14) The number of sunny days over the 100 years on record in Coast City has

a normal distribution. If the mean number of sunny days is 298 and 16 of

the years on record had at least 312 sunny days, what is the standard

deviation?

A) 10

B) 12

C) 14

D) 16

E) 28

15) The number of snow days in Mapleton has a normal distribution. If 3 of

the years on record had more than 31 snow days, the sum of the snow days

on record is 3750, and the mean number of snow days is 25, how many

years had more than 28 snow days?

A) 16

B) 22

C) 24

D) 25

E) 28

Explanations: 1) Answer: 10

To solve this question, draw the bell curve. Label the lowest point as 70, the mean as 100, and

the highest as 130. Since there are three intervals between the low point and the mean, and

100 – 70 = 30, the standard deviation must be 30 / 3 = 10.

2) Answer: B

To solve this question, draw the bell curve. Label the mean as 50, the next point to the

left as 45, and the point to the right as 55. Repeat for the remaining point. The range is 35

to 65.

3) Answer: D

To solve this question, draw the bell curve. Label the lowest point as 0 and the highest as

120. Since the standard deviation is 20, the points are 0 + 20 = 20, 20 + 20 = 40, et cetera.

Therefore the mean is 60.

4) Answer: A

To solve this question, draw the bell curve. Label the mean as 60. 32 out of 200 is 16%,

which is two right most standard deviations from the mean. Therefore the standard

deviation is 70 – 60 = 10.

5) Answer: D

To solve this question, draw the bell curve. Label the second to the left point as 22. Since

the mean is 24, the standard deviation is 1. Now since 14% + 2% = 16% score above a

25. Since 16% of 300 is 48, there are 48 student who scored above a 25.

6) Answer: 2

To solve this question, draw the bell curve. Label the lowest point as 60, the mean as 66,

and the highest as 72. Since there are three intervals between the low point and the mean,

and 66 – 60 = 6, the standard deviation must be 6 / 3 = 2.

7) Answer: D

To solve this question, draw the bell curve. Label the mean as 50, the next point to the

left as 45, and the point to the right as 55. Repeat for the remaining point. The range is 35

to 65.

8) Answer: C

To solve this question, draw the bell curve. Label the lowest point as 56 and the highest

as 65. Since the standard deviation is 1.5, the points are 56 + 1.5 = 57.5, 57.5 + 1.5 = 59,

et cetera. Therefore the mean is 60.5.

9) Answer: E

To solve this question, draw the bell curve. Label the mean as 67. 48 out of 300 is 16%,

which is two left most standard deviations. Therefore the standard deviation is 67 – 62 =

5.

10) Answer: C

To solve this question, draw the bell curve. Since the mean is 78 and 2% are above 84,

the standard deviation is 3. Now since 14% are between 72 and 75, and 14% of 300 = 42,

42 players are between 72 and 75 inches tall.

11) Answer: 2

To solve this question, draw the bell curve. Label the lowest point as 0, the mean as 6,

and the highest as 12. Since there are three intervals between the low point and the mean,

and 6 – 0 = 6, the standard deviation must be 6 / 3 = 2.

12) Answer: C

To solve this question, draw the bell curve. Label the mean as 100, the next point to the

left as 95, and the point to the right as 105. Repeat for the remaining point. The range is

85 to 115.

13) Answer: E

To solve this question, draw the bell curve. Label the lowest point as 26 and the highest

as 38. Since the standard deviation is 2, the points are 26 + 2 = 28, 28 + 2 = 30, et cetera.

Therefore the mean is 32.

14) Answer: C

To solve this question, draw the bell curve. Label the mean as 298. 16 out of 100 is 16%,

which is the two right most standard deviation of the mean. Therefore the standard

deviation is 312 – 298 = 14.

15) Answer: C

To solve this question, draw the bell curve. Since the total is 3750, and the mean is 25,

the number of years is 150. Therefore since 3 out of 150 is 2%, label the second to the

right point as 31. Since the mean is 25, and 31 – 25 = 6, the standard deviation is 6 / 2 =

3. Now since 14% + 2% = 16%, and 16% of 150 = 24, there were 24 years with more

than 28 snow days.