The Normal Distribution Worksheet - Oxford Insight Mathematics General Hsc General 2 Student Book Page 20
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
207 For a normal distribution, state the percentage of scores that have a z-score between:
a z = 0 and z = 1
b z = 0 and z = 2
c z = 1 and z = 2
d z = 2 and z = 3.
8 The average life of a particular brand of car battery is 4 years and 6 months with a standard deviation of
9 months. The manufacturer guarantees to replace any battery that does not last 3 years. If the life of these
batteries is normally distributed, approximately what percentage could the manufacturer expect to replace?
9 Packets of rice are fi lled and labelled as having a weight of 1 kg. The weight of these packets is normally
distributed with a mean of 1.05 kg and a standard deviation of 0.02 kg.
a Complete the following table.
Weight (kg)
0.99
1.01
1.03
1.05
1.07
1.09
1.11
z-score
0
1
b What percentage of packets will have a weight of less than 1.05 kg?
c What percentage of packets will have a weight between 1.03 kg and 1.07 kg?
d What percentage of packets will have a weight between 1.05 and 1.07 kg?
e What percentage of packets will have a weight between 1.01 kg and 1.09 kg?
f What percentage of packets will have a weight greater than 1.07 kg?
g What percentage of packets will have a weight less than the labelled weight?
6
EXAMINATION QUESTION (15 MARKS)
a A class test has a mean of 38 and standard deviation of 4.
i
Calculate the z-score for a mark of 46.
(1 mark)
ii
Calculate the z-score for a mark of 33.
(1 mark)
Calculate the mark for a z-score of −1.5.
iii
(1 mark)
b Ally scored 54 in the half-yearly exam for which the mean was 70 and the standard
deviation was 11. In the yearly exam the mean was 62 and standard deviation was 6.
Ally scored 58. Did Ally improve? Justify your answer.
(2 marks)
c The table shows the frequency distribution of data.
Score
8
9
10
11
12
13
14
15
Frequency
2
6
12
13
14
11
7
3
i
Draw a frequency histogram and polygon.
(2 marks)
ii
Calculate the mean, mode and median.
(2 marks)
iii
Is the distribution normal? Explain your answer.
(1 mark)
d A normal distribution has a mean of 20 and standard deviation of 3.
i
What percentage of scores lie between 17 and 23?
(1 mark)
ii
What percentage of scores are greater than 23?
(2 marks)
e Pancakes are made by a machine and their weights are normally distributed
with a mean of 39 g and a standard deviation of 1.5 g. A pancake weighing 44 g
is produced. Is the machine functioning properly? Explain your answer.
(2 marks)
218
Insight Mathematics General 12
HSC Course 2
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education