To determine how well the MBA student performed relative to her peers, we can use the concept of z-scores, which indicate how many standard deviations a score is from the mean.

The formula for the z-score is:

$z = \frac{(X - \mu)}{\sigma}$

where:

• $X$ is the student's score,
• $\mu$ is the mean score of the exam,
• $\sigma$ is the standard deviation of the exam scores.

Economics Exam

• Student's score ($X$): 81
• Mean ($\mu$): 70
• Standard Deviation ($\sigma$): 77

Calculating the z-score for economics:

$z_{econ} = \frac{(81 - 70)}{77} = \frac{11}{77} \approx 0.1429$

Math Exam

• Student's score ($X$): 87
• Mean ($\mu$): 70
• Standard Deviation ($\sigma$): 1111

Calculating the z-score for math:

$z_{math} = \frac{(87 - 70)}{1111} = \frac{17}{1111} \approx 0.0153$

Comparison

• Economics z-score: ≈ 0.1429
• Math z-score: ≈ 0.0153

Conclusion

The student performed better relative to her peers in economics, as her z-score (0.1429) is higher than that in math (0.0153).

Would you like more details on z-scores or further analysis? Here are some related questions you might consider:

1. What does a higher z-score indicate about a student's performance?
2. How do standard deviations impact the interpretation of exam scores?
3. Can z-scores be used for other types of comparisons, such as between different subjects?
4. What are some limitations of using z-scores for performance comparison?
5. How can students use z-scores to identify areas for improvement?

Tip: Always consider the context of the data when interpreting z-scores; they provide a relative measure but do not reflect the absolute scores' significance.