1. Given µ = 50 and σ = 15 calculate Z scores for the following values of X:
a. X = 25
b. X = 55
c. X = 35
2. Assume that the scores in question 1 follow the normal distribution. Calculate percentile scores for the three values of X in question 1.
3. Assume the distribution of scores in question 1 was transformed such that it would have a mean of 100 and a standard deviation of 10. What would be the transformed values of the three scores listed in question 1?
4. Calculate the X scores given the following Z scores.
a. Z = 1, µ = 30, σ = 5
b. Z = -1, µ = 25, σ = 10
c. Z = -.50, µ = 100, σ = 15
5. Given a sample of 40 first year psychology students with a mean age of 20 and a standard deviation of 4, for each of the following ages, calculate (1) the Z score, (2) the proportion of scores above and (3) the proportion of scores below for each of the following ages:
a. 19
b. 22
c. 28
6. Given the following information, µ = 60, σ = 10 what proportion of scores would fall between each of the following pairs of scores:
a. 55-70
b. 30-50
c. 65-80
7. The Mean and Standard Deviation on 6 scales of a standardized test and scores received by Fabio are presented in the Table below.
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Clerical Ability
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Logical Reasoning
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Mechanical Ability
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Numerical Reasoning
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Spatial Relations
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Verbal Fluency
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Score
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41
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47
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100
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105
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90
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70
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Mean
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50
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40
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120
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100
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70
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60
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S.D.
|
15
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4
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25
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10
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20
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6
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a) Calculate Z-scores for Fabio on each on the 6 tests.
b) Calculate percentile ranks on each test using Table B.1 in your textbook, and show all normal distribution curves with appropriate labels.
c) Create a bar graph with Fabio's Raw scores and Z-scores on all 6 tests.
d) On which of the 6 tests does Fabio perform the best?
8. Calculate the values beyond which fall the lowest 5% and the highest 5% of the scores on a variable with a Mean = 500 and a Standard Deviation = 100. Show all your work.