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To solve this problem, we need to determine how many standard deviations the student's scores in economics and mathematics are from the respective means, and then compare the results.

Let's calculate each score's Z-score, which measures how many standard deviations a given value is from the mean:

### Given Data:
1. **Economics:**
   - Score: \( 84 \)
   - Mean: \( 70 \)
   - Standard Deviation: \( 9 \)

2. **Mathematics:**
   - Score: \( 85 \)
   - Mean: \( 67 \)
   - Standard Deviation: \( 14 \)

### Calculations:

#### Step 1: Calculate Z-score for Economics
\[
Z_{\text{economics}} = \frac{\text{Score} - \text{Mean}}{\text{Standard Deviation}} = \frac{84 - 70}{9} = \frac{14}{9} \approx 1.56
\]

#### Step 2: Calculate Z-score for Mathematics
\[
Z_{\text{mathematics}} = \frac{\text{Score} - \text{Mean}}{\text{Standard Deviation}} = \frac{85 - 67}{14} = \frac{18}{14} \approx 1.29
\]

### Interpretation:
- The Z-score in economics is approximately \( 1.56 \).
- The Z-score in mathematics is approximately \( 1.29 \).

Since the Z-score in economics is higher than in mathematics, this means the student scored better relative to other students in economics than in mathematics.

### Answer:
The completed response should be:
> Since she scored **1.56** standard deviations **above** the mean in economics and **1.29** standard deviations **above** the mean in mathematics, she did better on the **economics** exam.

Would you like further details or have any questions?

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Here are five related questions to expand your understanding:

1. How does the Z-score help compare scores from different distributions?
2. What does a Z-score of 0 mean in terms of the student's performance?
3. How would the interpretation change if the Z-score in mathematics were higher than in economics?
4. How does changing the standard deviation affect the Z-score?
5. Why is it important to round to two decimal places in statistics?

**Tip:** Z-scores provide a standard way to compare scores across different scales by showing their position relative to the mean in terms of standard deviations.

An incoming MBA student took placement exams in economics and mathematics. In economics, she scored 84 and in math 85. The overall results on the economics exam had a mean of 70 and a standard deviation of 9, while the mean math score was 67, with a standard deviation of 14. On which exam did she do better compared with the other students?

Learn how to compare an MBA student's exam performance in economics and mathematics using Z-scores. The student's scores of 84 in economics and 85 in math are evaluated against the mean scores of 70 and 67, with standard deviations of 9 and 14, respectively. This analysis covers key statistical concepts, including Z-scores and standard deviations, suitable for undergraduate statistics.

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