sat scores the national average sat score (for verbal and math) is 1028. assume a normal distribution with $\sigma = 92$. use the standard normal distribution table. round intermediate $z$-value calculations to two decimal places.

part: 0 / 2

part 1 of 2

(a) what is the $65^{\text{th}}$ percentile score? round the answer to the nearest whole number.

the $65^{\text{th}}$ percentile score is .

Question

sat scores the national average sat score (for verbal and math) is 1028. assume a normal distribution with $\sigma = 92$. use the standard normal distribution table. round intermediate $z$-value calculations to two decimal places.

part: 0 / 2

part 1 of 2

(a) what is the $65^{\text{th}}$ percentile score? round the answer to the nearest whole number.

the $65^{\text{th}}$ percentile score is  .

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Normal Distribution", "Z-score Calculation", "Standard Normal Table" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Z-score Calculation", "Standard Normal Table", "Percentiles" ] } ## Identify given parameters $$ \begin{aligned} \mu &= 1028 \ \sigma &= 92 \ P &= 0.65 \end{aligned} $$ ## Find the corresponding z-score $$ \begin{aligned} P(Z < z) &= 0.65 \ z &\approx 0.39 \end{aligned} $$ ## Calculate the 65th percentile score $$ \begin{aligned} X &= \mu + z \cdot \sigma \ X &= 1028 + 0.39 \cdot 92 \ X &= 1028 + 35.88 \ X &= 1063.88 \approx 1064 \end{aligned} $$ (a) What is the $65^{\text{th}}$ percentile score? Round the answer to the nearest whole number. The $65^{\text{th}}$ percentile score is 1064. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Normal Distribution" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given parameters

Find the corresponding z-score

Calculate the 65th percentile score

Answer: