Sarah​'s score on the Stats midterm was 6464 points. The class average was 7474 and the standard deviation was 55 points. What was her​ z-score?

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

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

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

Given:
- Sarah's score, \( X = 6464 \),
- Class average, \( \mu = 7474 \),
- Standard deviation, \( \sigma = 55 \).

Now, plug in the values:

\[
z = \frac{6464 - 7474}{55}
\]

\[
z = \frac{-1010}{55}
\]

\[
z \approx -18.36
\]

### Conclusion:
Sarah's z-score is approximately \( -18.36 \).

Would you like to know more about how to interpret z-scores, or do you have any other questions?

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Here are some related questions:
1. What does a z-score of -18.36 indicate about Sarah’s performance relative to the class?
2. How would her z-score change if the class average were higher?
3. What does a negative z-score generally signify?
4. How is the standard deviation related to z-scores?
5. How can z-scores be used to identify outliers?

**Tip:** The z-score indicates how many standard deviations a value is from the mean.

Sarah's score on the Stats midterm was 6464 points. The class average was 7474 and the standard deviation was 55 points. What was her z-score?

Find out how to calculate Sarah's z-score based on her midterm score of 6464, with a class average of 7474 and a standard deviation of 55. This detailed solution covers essential statistical concepts, including z-scores and standard deviation, ideal for high school students.

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