1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions?
2. For the following set of scores, fill in the cells. The mean is 70 and the standard deviation is 8.
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Raw score
|
Z score
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68.0
|
?
|
|
?
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-1.6
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82.0
|
?
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|
?
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1.8
|
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69.0
|
?
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|
?
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-0.5
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85.0
|
?
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|
?
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1.7
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72.0
|
?
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3. Questions 3a through 3d are based on a distribution of scores with and the standard deviation = 6.38. Draw a small picture to help you see what is required.
a. What is the probability of a score falling between a raw score of 70 and 80?
b. What is the probability of a score falling above a raw score of 80?
c. What is the probability of a score falling between a raw score of 81 and 83?
d. What is the probability of a score falling below a raw score of 63?
4. Jake needs to score in the top 10% in order to earn a physical fitness certificate. The class mean is 78 and the standard deviation is 5.5. What raw score does he need?
5. Who is the better student, relative to his or her classmates? Use the following table for information.
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Math
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|
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Class mean
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81
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|
|
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Class standard deviation
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2
|
|
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Reading
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|
|
|
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Class mean
|
87
|
|
|
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Class standard deviation
|
10
|
|
|
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Raw scores
|
|
|
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Math score
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Reading score
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Average
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Noah
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85
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88
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86.5
|
|
Talya
|
87
|
81
|
84
|
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Z-scores
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|
|
|
|
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Math score
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Reading score
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Average
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|
Noah
|
|
|
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Talya
|
|
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