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The question asks for Gregor's score on a statistics midterm, given his **z-score** of -2, the **average score** (mean) of 80 points, and the **standard deviation** of 5 points.

The formula to calculate the actual score from a z-score is:

\[
X = \mu + z \cdot \sigma
\]

Where:
- \( X \) is Gregor's score.
- \( \mu \) is the mean (80 points).
- \( z \) is the z-score (-2).
- \( \sigma \) is the standard deviation (5 points).

Substitute the given values into the formula:

\[
X = 80 + (-2) \cdot 5
\]
\[
X = 80 - 10 = 70
\]

Thus, Gregor scored **70 points**.

Would you like further details or explanations? Here are five related questions to explore:

1. What does a negative z-score indicate in statistics?
2. How is a z-score interpreted in terms of standard deviations from the mean?
3. How would Gregor’s score change if his z-score was -1 instead of -2?
4. If the standard deviation was 10 instead of 5, how would Gregor's score be affected?
5. How can z-scores be used to compare results from different distributions?

**Tip:** Z-scores can help standardize different data points, allowing comparisons across different scales or datasets.

The average score on the Stats midterm was 80 points with a standard deviation of 5 points, and Gregor’s z-score was -2. How many points did he score?

Learn how to calculate Gregor's score on a statistics midterm given a z-score of -2, with a mean of 80 points and a standard deviation of 5 points. This problem demonstrates the use of the z-score formula and is suitable for college-level statistics students.

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