apply the empirical rule

| age | mean | standard deviation |
|---|---|---|
| 7 years | 49 inches | 2 inches |

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 inches and inches tall.

Question

apply the empirical rule

| age | mean | standard deviation |
|---|---|---|
| 7 years | 49 inches | 2 inches |

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   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" ] } ## Identify the given parameters Using the *Empirical Rule* knowledge point $$ \begin{aligned} &\mu = 49\text{ inches}\ &\sigma = 2\text{ inches} \end{aligned} $$ ## Apply the interval for 95% Using the *Empirical Rule* knowledge point $$ \begin{aligned} &\text{Interval} = [\mu - 2\sigma, \mu + 2\sigma]\ &\text{Lower Limit} = 49 - 2(2) = 45\ &\text{Upper Limit} = 49 + 2(2) = 53 \end{aligned} $$ 95% of 7-year-old children are between 45 inches and 53 inches tall. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Empirical Rule" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given parameters

Apply the interval for 95%

Answer: