The average score on the Stats midterm was 72 points with a standard deviation of 6 points, and FranzFranz​'s ​z-score was 1. How many points did he​ score?
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Part 1
He scored  enter your response here poin

To find Franz's score using the z-score formula, you can use the following equation:

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

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

Given:
- \( z = 1 \)
- \( \mu = 72 \)
- \( \sigma = 6 \)

Now, rearranging the formula to solve for \( X \):

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

Substituting the known values:

\[
X = 1 \cdot 6 + 72 = 6 + 72 = 78
\]

So, Franz scored **78 points**.

### Questions for Further Understanding:
1. How do you interpret a z-score in terms of performance relative to the average?
2. What would Franz's score be if his z-score were 2 instead of 1?
3. How does the standard deviation affect the spread of scores in a dataset?
4. Can you explain how to calculate the mean from a set of scores?
5. What implications does a low standard deviation have on the consistency of scores?

### Tip:
Understanding z-scores can help you compare scores from different distributions, as they standardize the data relative to the mean and standard deviation.

The average score on the Stats midterm was 72 points with a standard deviation of 6 points, and Franz's z-score was 1. How many points did he score?

Explore how to calculate a student's score using z-scores in statistics. Given an average score of 72 points and a standard deviation of 6 points, learn how to find that Franz scored 78 points with a z-score of 1. Ideal for students in Grades 9-12.

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