The average score on the Stats midterm was 72 points with a standard deviation of 66 ​points, and FranzFranz​'s ​z-score was 11. How many points did he​ score?
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Part 1
He scored  enter your response here points.

To find Franz's score, we can use the formula for calculating the z-score:

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

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

Given:
- \( z = 11 \)
- \( \mu = 72 \)
- \( \sigma = 66 \)

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

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

Now, substitute the values:

\[
X = 11 \cdot 66 + 72
\]
\[
X = 726 + 72
\]
\[
X = 798
\]

Franz scored **798 points**.

If you have any questions or need further details, feel free to ask! Here are some follow-up questions:

1. What does a high z-score indicate about a student's performance?
2. How would you interpret a negative z-score?
3. What would Franz's score need to be to have a z-score of 0?
4. How do you calculate the standard deviation from a data set?
5. What are some other statistical measures besides mean and standard deviation? 

**Tip:** Always consider the context of z-scores in relation to the overall distribution of scores.

The average score on the Stats midterm was 72 points with a standard deviation of 66 points, and Franz's z-score was 11. How many points did he score?

Discover how to calculate a student's score based on their z-score, with an average of 72 points and a standard deviation of 66 points. Learn the z-score formula and how it applies in this statistics problem. Ideal for students in Grades 10-12.

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