Sarah’s score on the stats midterm was 64 points. The class average was 74 and the standard deviation was 5 points. What was her z score?

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

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

where:
- \( X \) is Sarah's score (64),
- \( \mu \) is the class average (74),
- \( \sigma \) is the standard deviation (5).

Substituting in the values:

\[
z = \frac{(64 - 74)}{5} = \frac{-10}{5} = -2
\]

So, Sarah’s z-score is **-2**.

Would you like more details on interpreting this z-score or have any questions?

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1. What does a negative z-score signify in statistics?
2. How can z-scores help in comparing scores from different distributions?
3. What is the probability associated with Sarah’s z-score?
4. How would the z-score change if Sarah’s score were closer to the mean?
5. How is a z-score used in identifying outliers?

**Tip:** A z-score tells you how many standard deviations a score is from the mean.

Find Sarah's z-score for her stats midterm with a score of 64, given a class average of 74 and a standard deviation of 5. This problem covers key statistical concepts, including z-scores and standard deviation, suitable for students in Grades 10-12.

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