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{ "quality": "incomplete", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Normal Distribution", "Z-score Calculation", "Normal Curve Area" ], "new_concepts": [], "current_concepts": [ "Normal Distribution", "Z-score Calculation", "Normal Curve Area" ] } ## Calculate the z-score $$ \begin{aligned} &\mu = 100,\quad \sigma = 15\ &\text{Since the graph is missing, we assume a standard test value.}\ &\text{For a typical review problem of this type, the boundary score is } x = 115.\ &z = \frac{x - \mu}{\sigma} = \frac{115 - 100}{15} = 1.00 \end{aligned} $$ ## Find the cumulative area $$ \begin{aligned} &P(Z < 1.00) \approx 0.8413 \end{aligned} $$ ## Determine the shaded area $$ \begin{aligned} &\text{If the shaded region is to the left of } 115:\ &\text{Area} = 0.8413\ &\text{If the shaded region is to the right of } 115:\ &\text{Area} = 1 - 0.8413 = 0.1587 \end{aligned} $$ Find the area of the shaded region. 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 area of the shaded region is 0.8413 (or 0.1587 depending on whether the shaded region is to the left or right of 115). { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Normal Curve Area" ] }

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Calculate the z-score

Find the cumulative area

Determine the shaded area

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