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To calculate Rebecca's z-score, we use the z-score formula:

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

where:
- \( X \) is the individual score (Rebecca's score, 82),
- \( \mu \) is the mean score (class average, 75),
- \( \sigma \) is the standard deviation (7).

Substitute the values:

\[
z = \frac{82 - 75}{7} = \frac{7}{7} = 1
\]

Rebecca's z-score is \( z = 1 \).

This means her score is 1 standard deviation above the class average.

Would you like further explanation on z-scores or how to interpret them?

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Here are some related questions to deepen your understanding:
1. What does a negative z-score indicate?
2. How does the standard deviation affect the z-score calculation?
3. What would Rebecca’s z-score be if her score was 90 instead?
4. How can z-scores be used to compare scores from different distributions?
5. What is the significance of a z-score of 0?

**Tip:** Z-scores are useful for understanding how far a data point is from the mean in units of standard deviation, making it easier to compare across different distributions.

Rebecca's score on the Stats midterm was 82 points. The class average was 75 and the standard deviation was 7 points. What was her z-score?

Learn how to calculate a z-score based on Rebecca's score of 82 on her stats midterm. Given the class average of 75 and a standard deviation of 7, this solution guides you through using the z-score formula to determine Rebecca's performance relative to the mean. Ideal for students in Grades 10-12.

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