The Normal Distribution Worksheet - Oxford Insight Mathematics General Hsc General 2 Student Book Page 18
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204 Draw two normal curves with the same mean but diff erent standard deviations.
5 Toothpicks are packaged in boxes with a mean of 98 and standard deviation of 4 toothpicks. What proportion of
boxes will contain between:
a 94 and 102 toothpicks?
b 90 and 106 toothpicks?
c 86 and 110 toothpicks?
6 A machine produces bolts with a mean length of 25 mm and standard deviation 0.6 mm. Any bolts shorter than
23.2 m or longer than 26.8 mm are rejected. What percentage of bolts made by this machine will be rejected?
7 The weights of a large sample of 18-year-old males is normally distributed with a mean of 74 kg and standard
deviation of 6.5 kg. Between what limits would you expect the weights of:
a the middle 68% of these males to lie?
b the middle 95% of these males to lie?
c almost all, 99.7%, of these males to lie?
8 For a normal distribution state the percentage of scores that have a z-score:
a between z = −2 and z = 2
b greater than z = 2
c less than z = 2
d less than z = −2
e greater than z = −2
6C
REVIEW SET
1 In a Commerce test the mean was 63 and the standard deviation was 12. Calculate the standardised scores for
test marks of:
a 81
b 39
c 66
d 58
2 The results for an examination had a mean score of 55 and a standard deviation of 10. Write the raw examination
mark corresponding to a standardised score of:
c −0.9
d −2.1
a 0.6
b 1.3
3 The following are the scores in a Language test:
60
61
59
50
65
77
63
58
36
88
66
74,
61
43
58
a Calculate the mean and standard deviation of these marks.
b How many scores lie within 1 standard deviation of the mean?
c How many scores are more than 2 standard deviations above the mean?
4 Francis scored 52 in the half-yearly English test for which the mean was 68 and the standard deviation 11. In the
yearly examination for which the mean was 60 and the standard deviation 6, she scored 56. Determine whether
or not Francis improved her performance in English over the year. Justify your answer.
5 Which of the following is a normal curve?
A
B
C
f
f
f
6 The life of a brand of electric light globe is normally distributed with a mean of 1400 hours and a standard
deviation of 120 hours. Within what limits would you expect:
a the middle 68% of globes to last?
b the middle 95% of globes to last?
c nearly all, 99.7%, of globes to last?
216
Insight Mathematics General 12
HSC Course 2
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