The average score on the Stats midterm was 74 points with a standard deviation of 5 points, and GregorGregor​'s ​z-score was negative −1. How many points did he​ score?
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Part 1
He scored  enter your response here

To find Gregor's score using his z-score, we can use the formula for the z-score:

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

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

Given:
- \( z = -1 \)
- \( \mu = 74 \)
- \( \sigma = 5 \)

We can rearrange the formula to solve for \( X \):

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

Substituting the values:

\[
X = (-1) \cdot 5 + 74
\]
\[
X = -5 + 74
\]
\[
X = 69
\]

Gregor scored **69 points**.

### Do you want details or have any questions?
Here are some related questions you might find interesting:
1. What does a negative z-score indicate about Gregor's performance compared to his peers?
2. How would Gregor's score change if the average and standard deviation were different?
3. Can you explain how to calculate z-scores for other scores in the same distribution?
4. What percentage of students scored above or below Gregor?
5. How does the standard deviation affect the interpretation of scores in a normal distribution?

**Tip:** Always remember that a z-score tells you how many standard deviations a value is from the mean, which can help assess performance relative to a group.

The average score on the Stats midterm was 74 points with a standard deviation of 5 points, and Gregor's z-score was negative −1. How many points did he score?

Discover how to calculate Gregor's score on the Stats midterm using his z-score of -1. With an average score of 74 and a standard deviation of 5, learn the step-by-step solution that reveals he scored 69 points.

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