Question

If a person got a score of 75 on a test, which of the following distributions allow(s) for the most favourable interpretation of that score? (assuming higher values are more favourable)

• A. Mean = 55, Standard Deviation = 4
• B. Mean = 60, Standard Deviation = 3
• C. Mean = 65, Standard Deviation = 5
• D. Mean = 50, Standard Deviation = 10

Hint:

A higher z-score means better relative performance, regardless of the raw score.

Answer 1

The Correct Option is A, B

Step 1: Use standard score (z-score) for comparison.
A score is interpreted more favourably when it lies many standard deviations above the mean.
Step 2: Compute relative standing.
(A): \( z = \frac{75-55}{4} = 5 \)
(B): \( z = \frac{75-60}{3} = 5 \)
(C): \( z = \frac{75-65}{5} = 2 \)
(D): \( z = \frac{75-50}{10} = 2.5 \)
Step 3: Compare outcomes.
Options (A) and (B) yield the highest z-scores, hence the most favourable interpretations.
Step 4: Conclusion.
The most favourable interpretations occur in distributions (A) and (B).