An incoming MBA student took placement exams in economics and mathematics. In​ economics, she scored 81 and in math 87. The overall results on the economics exam had a mean of 70 and a standard deviation of 77​, while the mean math score was 70​, with a standard deviation of 1111. On which exam did she do better compared with the other​ students?

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.

Discover how to compare exam scores using z-scores. An MBA student scored 81 in economics (mean 70, SD 77) and 87 in math (mean 70, SD 1111). Learn which subject she performed better in relative to her peers.

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