PSY 429 Experimental Psychology

Class Exercise #2

Standard Scores (z scores)

Answers

1. What is the mean and standard deviation of a z-score distribution?

 The mean is 0 and the standard deviation is 1.0

2. What is the z-score formula for a population?

  z = (X - m ) / s

 

3. What is the z-score formula for a sample?

 z = (X - M ) / s

4. A distribution of general psychology test scores has a mean of m = 60 and a standard deviation of s = 4. What is the z-score for Scott who received a 66? (Assume the distribution of test scores was normal.)

 z = (X - m ) / s

z = 66 - 60 / 4

z = 1.5

5. What proportion of scores lies above Scott's score of 66?

[See Table 2]

 .0668 or 6.68% of scores lies above a score of 66

6. The distribution of SAT verbal scores for high school seniors has a mean of m = 500 and a standard deviation of s = 100. Joe took the SAT and scored 430 on the verbal subtest. What is the z-score which corresponds to Joe's score of 430?

z = (X - m ) / s

z = 430 - 500 / 100

z = - .70

a. What percentage of people fell below Joe?

[See Table 2]

.2420 or 24.2% of the scores fell below Joe's score of 66

b. What percentage of people fell above Joe?

[See Table 2]

 .7580 or 75.8% of the scores fell above Joe's score of 66

7. Given a normally distributed variable with a m = 50 and a s = 10, what proportion of scores falls below a score of 30?

z = (X - m ) / s

z = 30 - 50 / 10

z = - 2.00

[See Table 2]

Therefore, .0228 or 2.28% of scores falls below a score of 30.

8. Given a normally distributed variable with a m = 50 and a s = 10, what proportion of scores falls between a score of 40 and a score of 55?

 z = (X - m ) / s

z = 40 - 50 / 10

z = - 1.00

[See Table 2]

Therefore, .3413 or 34.13% of scores lie between a score of 40 and the mean.

z = (X - m ) / s

z = 55 - 50 / 10

z = .50

[See Table 2]

Therefore, .1915 or 19.15% of scores lie between a score of 55 and the mean.

Consequently, 53.28% (34.13% + 19.15%) of scores lie between a score of 40 and a score of 55.

9. Given a normal distribution of a sample with a M = 48 and a S = 10 and an n = 300, find the number of cases that would fall below a score of 44.

 z = (X - M ) / s

z = 44 - 48 / 10

z = - .40

[See Table 2]

.3446 or 34.46% of scores fall below a score of 44.

To find the number of cases below a score of 44, multiply .3446 by 300.

.3446 x 300 = 103.38 or 103 cases fall below a score of 44.

10. Given a normally distributed variable with a M = 50 and a S = 10, what proportion of scores falls between a score of 35 and a score of 40?

  z = (X - M ) / s

z = 35 - 50 / 10

z = - 1.50

[See Table 2]

Therefore, .4332 or 43.32% of scores lie between a score of 35 and the mean.

z = (X - M ) / s

z = 40 - 50 / 10

z = - 1.00

[See Table 2]

Therefore, .3413 or 34.13% of scores lie between a score of 40 and the mean.

Consequently, .0919 (43.32% - 34.13%) of scores lie between a score of 35 and a score of 40.

11.Find the score that separates the upper 20% from the lower 80% if the mean is 50 and the standard deviation is 10.

20% of scores lie above this score (X)

Find z score associated with upper 20%.

[See Table 2]

Looking at z table, the z score associated with the upper 20% is .84.

Given the formula z = (X - m ) / s

then X = m + z(s)

X = 50 + .84(10)

X = 58.4

Psy 429 Main Page	Syllabus	Class Exercises	Homework Assign.	Experimental Dilemmas	Sample Tests;Answers	Statistical Tables
Learning Objectives	Statistical Formula	Answers to Class Ex.	Answers to Homework	Answers to Dilemmas	Web Links	Additional Exercises

To go back to Dr. Ryan's Home Page, click on kitty.

 

 

Celtic Clip Art - http://artinfo@aon-celtic.com