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To find Gregor's score based on the given information, we use the formula for a z-score:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \( z \) is the z-score,
- \( X \) is Gregor's score,
- \( \mu \) is the mean score,
- \( \sigma \) is the standard deviation.

### Given dataTo find Gregor's score based on the given information, we use the formula for a z-score:

\[
z = \frac{X - \mu}{\sigma}
\]

where:
- \( z \) is the z-score,
- \( X \) is Gregor's score,
- \( \mu \) is the mean score,
- \( \sigma \) is the standard deviation.

### Given 
- \( \mu = 72 \) (average score),
- \( \sigma = 5 \) (standard deviation),
- \( z = -2 \) (Gregor's z-score).

### Solution:

Rearrange the formula to solve for \( X \):

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

Substitute the values:

\[
X = (-2) \cdot 5 + 72
\]
\[
X = -10 + 72
\]
\[
X = 62
\]

### Answer:
Gregor scored **62 points**.

Would you like further details or have any questions?

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Here are five related questions for practice:
1. If a student’s z-score was 1.5 on the same test, what was their score?
2. How would Gregor's score change if the standard deviation was 10 points instead?
3. What score corresponds to a z-score of 0 in this scenario?
4. If Gregor’s score was 5 points lower, what would his new z-score be?
5. What is the interpretation of a z-score of -2 in terms of Gregor's performance?

**Tip:** Remember, a negative z-score means the score is below the mean.

The average score on the Stats midterm was 72 points with a standard deviation of 5 points, and Gregor's z-score was -2. How many points did he score?

Learn how to determine a student's score on a statistics midterm using the z-score formula. Given a mean of 72, standard deviation of 5, and z-score of -2, find Gregor's score through a step-by-step solution.

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