Lets say you got 235 on this test. Your college is in a different section of this course. Her score was 82 out of 100 on her test. In her section the mean was 72 and the standard deviation was 7. Which one of you did better?

To determine who did better, we need to compare the respective scores in relation to the mean and standard deviation of each section. Here's the step-by-step process:

1. Calculate the Z-score for each score.
The Z-score measures how many standard deviations a particular score is away from the mean. The formula for calculating the Z-score is:

Z = (X - μ) / σ

Where:
- X is the individual score
- μ is the mean of the section
- σ is the standard deviation of the section

For your score of 235 in your section:
Z = (235 - μ_yourSection) / σ_yourSection

For her score of 82 in her section:
Z = (82 - μ_herSection) / σ_herSection

2. Determine the Z-scores.
Using the given mean and standard deviation values, plug in the respective values to calculate the Z-scores for each score.

For your score:
Z_yourSection = (235 - μ_yourSection) / σ_yourSection

For her score:
Z_herSection = (82 - μ_herSection) / σ_herSection

3. Compare the Z-scores.
The Z-scores allow us to compare the relative position of each score within their respective sections. A higher Z-score indicates a better performance relative to the section mean, while a lower Z-score indicates a lower performance.

If your Z-score is higher than her Z-score, you performed better. If her Z-score is higher, she performed better.

Note: Z-scores greater than 0 indicate scores above the mean, while Z-scores less than 0 indicate scores below the mean.

By following these steps and calculating the Z-scores for both of your scores, you can determine which one of you performed better in relation to your respective course sections.