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Normal Distribution Empirical

Total questions: 23

Worksheet time: 55mins

Name
Class
Date
1.
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 
a)
1084 to 1216 pounds 
b)
1106 to 1150 pounds 
c)
1106 to 1194 pounds 
d)
1128 to 1172 pounds
2.
The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.
a)
 28,000 km and 32,000 km.
b)
24,000 km and 34,000 km.
c)
26,000 km and 34,000 km.
d)
27,000 km and 31,000 km.
3.
Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
4.
Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 
a)
9 to 21
b)
12 to 18
c)
6 to 24
d)
13 to 16
5.

Which interval shows 99.7% of the data given a mean of 15 and a standard deviation of 3?

a)

9 to 21

b)

12 to 18

c)

6 to 24

d)

13 to 16

6.

What percent of the data falls within 3 standard deviations of the mean?

a)

99.7

b)

34

c)

68

d)

95

7.

What percent of the data falls within 2 standard deviations of the mean?

a)

99.7

b)

34

c)

68

d)

95

8.

What percent of the data falls within 1 standard deviation of the mean?

a)

99.7

b)

34

c)

68

d)

95

9.
The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days.

About what percent of the products last between 12 and 15 days?
a)
68%
b)
34%
c)
16%
d)
2.5%
10.
At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?
a)
68%
b)
99.7%
c)
95%
d)
84%
11.

Use the following information and the Empirical Rule to estimate the answer.


The ages of golfers are normally distributed, with a mean of 38 and a standard deviation of 4.


Find the proportion of golfers that are between 30 and 46 years old.

a)

68%

b)

94%

c)

95%

d)

99.7%

12.
What is the Normal Range (68%) of the annual precipitation for Phoenix, if the average is 29 with a standard deviation of 3?
a)
26-32
b)
3-29
c)
26-29
d)
39-32
13.
The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. What percent of students in the course have a GPA between  2.9 and 3.8? 
a)
81.5%
b)
47.5%
c)
68%
d)
95%
14.

Given a mean of 75 and a standard deviation of 7, what percentage of scores are above 82?

a)

34%

b)

81.5%

c)

16%

d)

2.5%

15.

In the diagram, about 68% of the scores fall within the shaded area, which is symmetric about the mean. The distribution is normal and scores in the area range from 50 to 80. What is the standard deviation of the scores in this distribution?

a)

7.5

b)

15

c)

30

d)

65

16.

If the mean height is 180cm and the standard deviation is 4. What percentage of the population would lie between 176cm and 184cm?

a)

34%

b)

68%

c)

95%

d)

50%

17.

If the mean height is 180cm and the standard deviation is 4. What percentage of the population would lie between 176cm and 180cm?

a)

34%

b)

68%

c)

95%

d)

50%

18.
The average waist size for teenage males is 29 inches with a standard deviation of 1.4 inch.  If waist sizes are normally distributed, estimate the proportion of teenagers who will have waist sizes greater than 31 inches?
a)
92.4%
b)
10.5%
c)
16%
d)
7.6%
19.

What Percent of the data lies between 60 and 90?

a)

50%

b)

81.5%

c)

68%

d)

99.7%

20.

35 is

a)

mean

b)

variance

c)

standard deviation

d)

1st quartile

21.

What is the standard deviation on this Normal Curve?

a)

6

b)

12

c)

34

d)

18

22.

If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

a)

20

b)

15

c)

40

d)

30

23.

If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

a)

40

b)

35

c)

45

d)

50