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To determine Franz's score based on his z-score, we can use the z-score formula:

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

where:
- \( z \) is the z-score,
- \( X \) is Franz's score (the unknown value we are solving for),
- \( \mu \) is the average score, and
- \( \sigma \) is the standard deviation.

Given:
- Average score (\( \mu \)) = 76 points,
- Standard deviation (\( \sigma \)) = 7 points,
- Franz's z-score (\( z \)) = 1.

Substitute the values into the formula:

\[
1 = \frac{X - 76}{7}
\]

Now, solve for \( X \):

1. Multiply both sides by 7:
   \[
   X - 76 = 7
   \]

2. Add 76 to both sides:
   \[
   X = 83
   \]

So, Franz scored **83 points**.

Would you like a more detailed explanation, or do you have any other questions?

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Here are some related questions:
1. What would Franz's score be if his z-score was 2?
2. How do you calculate the z-score if you know a score and the mean?
3. What is a standard deviation and why is it important in statistics?
4. How would the score change if the standard deviation were different?
5. Can z-scores be negative, and what would that indicate?

**Tip:** Z-scores indicate how far a value is from the mean in terms of standard deviations, providing insight into its relative position within a distribution.

The average score on the Stats midterm was 76 points with a standard deviation of 7 points, and Franz's z-score was 1. How many points did he score?

Find out how to calculate Franz's score based on a z-score of 1, with an average score of 76 points and a standard deviation of 7 points. Learn how to use the z-score formula to solve statistical problems. Suitable for college-level statistics students.

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