the graph to the right depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
click to view page 2 of the table.

n is (round to four decimal places as needed.)

Question

the graph to the right depicts iq scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
click to view page 2 of the table.

n is   (round to four decimal places as needed.)

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", "Cumulative Probability" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Z-score Calculation", "Cumulative Probability" ] } ## Calculate the z-score for the given IQ score $$ \begin{aligned} \mu &= 100 \ \sigma &= 15 \ x &= 120 \ z &= \frac{x - \mu}{\sigma} = \frac{120 - 100}{15} = \frac{20}{15} \approx 1.3333 \end{aligned} $$ ## Find the cumulative area to the left of the z-score $$ \begin{aligned} P(X < 120) &= P(Z < 1.3333) \ \Phi(1.3333) &\approx 0.9088 \end{aligned} $$ The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. The shaded area shown is 0.9088 (Round to four decimal places as needed.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Normal Curve Area" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the z-score for the given IQ score

Find the cumulative area to the left of the z-score

Answer: