Question

Computation of z-scores and standardized scores

You are a school psychologist and have been asked to administer a verbal intelligence test to a local senior high school English class to assess writing preparedness of the class. You have been given the mean (μ = 70) and population standard deviation (σ = 8) for the raw scores from this test. Based on the testing manual, you know that the developers of this assessment generate a standardized score using a predetermined mean of 100 and standard deviation of 25. Answer the following questions about the scores below.

1. Annie’s raw exam score is 80. What is Annie’s z-score?_________________

2. Ryan’s raw score is 66. What is Ryan’s z-score?_________________

3. Casey’s raw score is 85. What is Casey’s standardized exam score?_________________
   4. Kaleigh’s standardized exam score is 95. What is Kaleigh’s raw exam score?_________________

5. Bailey’s z-score is 1.5. What is Bailey’s standardized score?________________

Answer 1

You have been given the mean (μ = 70) and population standard deviation (σ = 8) for the raw scores from this test. Based on the testing manual, you know that the developers of this assessment generate a standardized score using a predetermined mean of 100 and standard deviation of 25.

1) If, Annie's raw exam score is 80, then Annie's z-score is,

Z = (80 - 70) / 8 = 10/8 = 1.25

z-score = 1.25

2) If Ryan's raw score is 66, the Ryan's z-score is,

Z = (66 - 70) / 8 = -4/8 = 0.50

z-score = -0.50

3) Casey's raw score is 85, then z-score is,

z = (85 - 70) / 8 = 15/8 = 1.875

Now, standardized score

= (1.875 * 25) + 100 = 46.875 + 100 = 146.875

Therefore, the Casey's standardized exam score is 146.875

4) Kaleigh's standardized exan score is 95, then z-score is,

z = (95 - 100) / 25 = -0.2

And raw exam score = (-0.2 * 8) + 70 = -1.6 + 70 = 68.4

Therefore, the Kaleigh's raw exam score = 68.4

5) Bailey's z-score is 1.5 then Bailey's standardized score is,

X = ( 1.5 * 25) + 100 = 37.5 + 100 = 137.5

Standardized score = 137.5