in the united states, birth weights of newborn babies are approximately normally distributed with a mean of $\mu = 3,500\text{ g}$ and a standard deviation of $\sigma = 500\text{ g}$.

according to the empirical rule, 68% of all newborn babies in the united states weigh between 3000 g and 4000 g.

95% of all newborn babies in the united states weigh between and .

Question

in the united states, birth weights of newborn babies are approximately normally distributed with a mean of $\mu = 3,500\text{ g}$ and a standard deviation of $\sigma = 500\text{ g}$.

according to the empirical rule, 68% of all newborn babies in the united states weigh between 3000 g and 4000 g.

95% of all newborn babies in the united states weigh between   and  .

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": [ "Normal Distribution", "Empirical Rule" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Empirical Rule" ] } ## Identify the given parameters Using the *Normal Distribution* knowledge point $$ \begin{aligned} \mu &= 3500\text{ g} \ \sigma &= 500\text{ g} \end{aligned} $$ ## Apply the empirical rule for 95% Using the *Empirical Rule* knowledge point $$ \begin{aligned} \text{Interval} &= \mu \pm 2\sigma \ \text{Lower Bound} &= 3500 - 2(500) = 2500\text{ g} \ \text{Upper Bound} &= 3500 + 2(500) = 4500\text{ g} \end{aligned} $$ 95% of all newborn babies in the United States weigh between 2500 g and 4500 g. { "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 95%

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