according to the empirical rule, 68% of 7-year-old children are between 47 inches and 51 inches tall.
95% of 7-year-old children are between 45 inches and 53 inches tall.
99.7% of 7-year-old children are between inches and inches tall.

Question

according to the empirical rule, 68% of 7-year-old children are between 47 inches and 51 inches tall.
95% of 7-year-old children are between 45 inches and 53 inches tall.
99.7% of 7-year-old children are between   inches and   inches tall.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Empirical Rule" ], "new_concepts": [], "current_concepts": [ "Empirical Rule", "Normal Distribution Spread" ] } ## Identify the given parameters Using the *Empirical Rule* knowledge point $$ \begin{aligned} \mu &= 49\text{ inches} \ \sigma &= 2\text{ inches} \end{aligned} $$ ## Apply the Empirical Rule for 99.7% Using the *Empirical Rule* knowledge point $$ \begin{aligned} \text{Interval} &= [\mu - 3\sigma, \mu + 3\sigma] \ \text{Lower bound} &= 49 - 3(2) = 49 - 6 = 43 \ \text{Upper bound} &= 49 + 3(2) = 49 + 6 = 55 \end{aligned} $$ 99.7% of 7-year-old children are between 43 inches and 55 inches tall. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Empirical Rule" ] }

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Explanation:

Identify the given parameters

Apply the Empirical Rule for 99.7%

Answer: