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.