Subjects statistics

Relative Performance

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Relative Performance


1. **State the problem:** We want to determine who performed better relative to their class by comparing Lisa's and Kevin's scores using z-scores. 2. **Formula for z-score:** $$z = \frac{X - \mu}{\sigma}$$ where $X$ is the individual score, $\mu$ is the class mean, and $\sigma$ is the standard deviation. 3. **Calculate Lisa's z-score:** $$z_{Lisa} = \frac{75 - 70}{5} = \frac{5}{5} = 1$$ 4. **Calculate Kevin's z-score:** $$z_{Kevin} = \frac{88 - 85}{2} = \frac{3}{2} = 1.5$$ 5. **Interpretation:** A higher z-score means better performance relative to the class. 6. **Conclusion:** Kevin's z-score (1.5) is higher than Lisa's (1), so Kevin performed better relative to his class.