Reference no: EM13874196

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.

	Clerical Ability	Logical Reasoning	Mechanical Ability	Numerical Reasoning	Spatial Relations	Verbal Fluency
Score	41	47	100	105	90	70
Mean	50	40	120	100	70	60
S.D.	15	4	25	10	20	6

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.