The Normal Distribution Worksheet - Oxford Insight Mathematics General Hsc General 2 Student Book Page 11
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20EXERCISE 6D
1
The marks on a test are normally distributed with a mean of 62 and a standard deviation of 5.
a
What mark is one standard deviation:
i
ii
above the mean?
below the mean?
Approximately what proportion of students scored a mark within ±1 standard deviation?
b
c
What mark is two standard deviations:
i
ii
above the mean?
below the mean?
Approximately what proportion of students scored a mark within ±2 standard deviations?
d
e
What mark is three standard deviations:
i
ii
above the mean?
below the mean?
Approximately what proportion of students scored a mark within ±3 standard deviations?
f
2
The life of a certain brand of torch batteries is normally distributed with a mean of 56 hours and standard
deviation of 2.6 hours.
a
Complete the following table.
Life (hours)
48.2
50.8
53.4
56
58.6
61.2
63.8
z-score
0
b
Approximately what proportion
of batteries have a life between:
i
48.2 h and 63.8 h?
ii
50.8 h and 61.2 h?
iii
53.4 h and 58.6 h?
3
The heights of 1000 Year 12 males are approximately normally distributed with a mean of 168 cm and standard
deviation of 9 cm. What percentage of students have heights between:
a
b
c
159 cm and 177 cm?
150 cm and 186 cm?
141 cm and 195 cm?
4
Use the given graphs of normal distributions to answer the following questions.
a
What percentage of scores have a z-score:
50%
50%
between −1 and 1?
i
ii
between 0 and 1?
between 0 and −1?
iii
iv
greater than 0?
v
vi
less than 0?
greater than 1?
68%
less than −1?
greater than −1?
vii
viii
ix
−3 −2
less than 1?
−1
0
1
2
3
z-score
b
What percentage of scores have a z-score:
50%
50%
between −2 and 2?
i
ii
between 0 and 2?
between 0 and −2?
iii
iv
greater than 2?
less than −2?
greater than −2?
v
vi
95%
vii
less than 2?
−3
−2 −1
2
3
0
1
z-score
Chapter 6
The normal distribution
209
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education