a newborn who weighs 2,500 g or less has a low birth weight. use the information on the right to find the z-score of a 2,500 g baby.
what is the z-score of a newborn who weighs 4,000 g?
what weight would give a newborn a z-score of -0.75? grams

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 $\sigma = 500\text{ g}$.

\z = \frac{x - \mu}{\sigma}\

Question

a newborn who weighs 2,500 g or less has a low birth weight. use the information on the right to find the z-score of a 2,500 g baby.
what is the z-score of a newborn who weighs 4,000 g?
what weight would give a newborn a z-score of -0.75?   grams

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 $\sigma = 500\text{ g}$.

\z = \frac{x - \mu}{\sigma}\

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": [ "Z-Score Formula" ], "new_concepts": [], "current_concepts": [ "Z-Score Formula", "Normal Distribution" ] } ## Identify given parameters Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &\mu = 3500\ &\sigma = 500\ &z = -0.75 \end{aligned} $$ ## Solve for the unknown weight Using the *Z-Score Formula* knowledge point $$ \begin{aligned} &z = \frac{x - \mu}{\sigma}\ &-0.75 = \frac{x - 3500}{500}\ &x - 3500 = -0.75 \cdot 500\ &x - 3500 = -375\ &x = 3125 \end{aligned} $$ What weight would give a newborn a z-score of $-0.75$? 3125 grams { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Z-Score Formula" ] }

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Question

Explanation:

Identify given parameters

Solve for the unknown weight

Answer: