Question

For a particular group of scores, M= 10 and SD= 2. Give the raw score for a Z score of (a) +2 (b) +.5 (c) 0 (d) -3.

a) (a) 14, (b) 11, (c) 10, (d) 4
b) (a) 12, (b) 10.5, (c) 10, (d) 4
c) (a) 8, (b) 11, (c) 10, (d) 4
d) (a) 12, (b) 9.5, (c) 10, (d) 4'

Answer 1

To find raw scores from z-scores, use the formula x = M + (z)(SD) for each z-score. This approach yields raw scores of 14, 11, 10, and 4 for z-scores of +2, +0.5, 0, and -3 respectively.

Step-by-step explanation:

In this scenario, a student needs to determine the raw scores corresponding to different z-scores given a mean (M=10) and a standard deviation (SD=2) of a data set. To convert a z-score to a raw score, the formula is x = M + (z)(SD). This formula illustrates that to find a specific data point, one adds the product of the z-score and the standard deviation to the mean.

• For a z-score of +2, the raw score is 10 + (2)(2) = 14.
• For a z-score of +0.5, the raw score is 10 + (0.5)(2) = 11.
• For a z-score of 0, the raw score is 10 + (0)(2) = 10.
• For a z-score of -3, the raw score is 10 + (-3)(2) = 4.

Correct Answers

1. (a) 14
2. (b) 11
3. (c) 10
4. (d) 4