wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Unit 1 - Normal Distribution & Z - Score

Total questions: 20

Worksheet time: 40mins

Name
Class
Date
1.
Four data sets are shown below.
Set 1: {10, 19, 38, 50, 51}
Set 2: {5, 21, 26, 39, 51}
Set 3: {9, 38, 50, 50, 51}
Set 4: {5, 28, 28, 28, 51}
Which data set has the largest standard deviation?
a)
Set 1
b)
Set 2
c)
Set 3
d)
Set 4
2.

What is the standard deviation for the data given:

5, 10, 7, 12, 0, 20, 15, 22, 8, 2

a)

6.89

b)

10.1

c)

7.26

d)

9

3.

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. Draw a normal curve on a separate piece of paper to help. *What test score is two standard deviation above the mean?*

a)

66

b)

86

c)

56

d)

96

4.

Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10. *In a group of 230 tests, how many students score below 66?* Round to the nearest whole number.

a)

37

b)

36

c)

78

d)

31

5.

The number of nails of a given length is normally distributed with a mean length of 5.00 inches and a standard deviation of .0.03 inches. What percent of nails in a bag that are less than 4.94?

a)

34%

b)

13.5%

c)

2.5%

6.

Snobby University accepts only those graduate students who score in the top 5% of the GRE (Graduate Requirements Exam).


Given that µ = 151.3 and σ = 8.7, what is the lowest score you can get and still be accepted to SU? Round to the nearest whole number.

a)

165

b)

166

c)

170

d)

162

7.
According to the empirical rule, how much of the data falls within 3 standard deviations? 
a)
25%
b)
68%
c)
95%
d)
99.7%
8.

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%

9.
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
10.
The mean number of accidents a week at a company is 6.4 with a standard deviation of 1.5.  What proportion of weeks would you expect to have less than 5 accidents?
a)
0.6915
b)
0.1753
c)
0.8238
d)
-0.93
11.
The average number of calories in a 1.5-ounce chocolate bar is 225.  Suppose that the distribution of calories is approximately normal with a σ of 10.  Find the probability that a randomly selected chocolate bar will have between 200 and 220 calories. 
a)
0.9876
b)
0.3023
c)
0.0098
d)
0.3320
12.

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 probability that a teenager will have a waist size greater than 31 inches.

a)

.924

b)

.105

c)

.16

d)

.076

13.

In Standford, CA, cars were traveling at a mean speed of 23.84 mph, with a standard deviation of 3.56 mph. One car's z-score was +3.2. How fast was that car going?

a)

72.728 mph

b)

12.448 mph

c)

35.232 mph

d)

32.563 mph

14.

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)

0.4013

b)

0.2403

c)

0.5204

d)

0.1407

15.

What is the area under the normal curve to the left of one standard deviation above the mean?

a)

0.16

b)

0.34

c)

0.50

d)

0.84

16.

On a standardized exam, the scores are normally distributed with a mean of 75 and a standard deviation of 10. Find the z-score of a person who scored 45 on the exam.

a)

-3

b)

3

c)

1.44

d)

2

17.

On a standardized exam, the scores are normally distributed with a mean of 500 and a standard deviation of 25. Find the z-score of a person who scored 525 on the exam.

a)

1

b)

-1

c)

0

d)

2

18.

Joanne's Z-score is -1.5. What does this mean?

a)

She didn't take the test yet.

b)

She scored 1.5 standard deviations below the average.

c)

She did better than most people.

d)

No clue

19.

A grading scale is set up for 1000 students’ test scores. It is assumed that the scores are normally distributed with a mean score of 75 and a standard deviation of 15. Calculate the score that has a z-score of -2.

a)

60

b)

475

c)

45

d)

9500

20.

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)

99.7%

c)

95%

d)

34%