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{ "quality": "blurry", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Normal Distribution", "Z-Score Formula", "Empirical Rule" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Z-Score Formula", "Empirical Rule" ] } ## Calculate the Z-score Using the *Z-Score Formula* knowledge point $$ z = \frac{x - \mu}{\sigma} = \frac{3.1 - 2.5}{0.6} = \frac{0.6}{0.6} = 1 $$ ## Determine the percentage using the Empirical Rule Using the *Empirical Rule* and *Normal Distribution* knowledge points $$ \begin{aligned} &P(Z > 1) = \frac{1 - P(-1 < Z < 1)}{2} = \frac{1 - 0.68}{2} = 0.16\ &\text{Percentage} = 16\% \end{aligned} $$

(A) 5%

(B) 10%

(C) 16%

(D) 32%

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Statistics", "Empirical Rule" ] }

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Explanation:

Calculate the Z-score

Determine the percentage using the Empirical Rule

Answer: