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VICMath MethodsQuick questions

Unit 4

Quick questions on The normal distribution: VCE Math Methods Unit 4

10short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is quality control?
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The lengths or weights of manufactured items are often modelled as normal with mean = target and standard deviation = tolerance. Questions ask for the proportion outside specification.
What is examinations and IQ?
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Scores on standardised tests are typically modelled as normal.
What is biology and medicine?
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Heights, blood pressure, gestation periods, biomarker levels are often approximately normal.
What is finance?
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Returns on a portfolio over a fixed period are sometimes modelled as normal (in basic Methods contexts; real finance uses heavier tails).
What is inverse direction error?
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"P(X>c)=0.10P(X > c) = 0.10" means cc is in the upper tail; "P(X<c)=0.10P(X < c) = 0.10" means cc is in the lower tail. Use 1−p1 - p if needed before invNorm.
What is empirical rule misapplied?
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The empirical rule is for μ±nσ\mu \pm n\sigma specifically. For other endpoints, standardise and use a table or calculator.
What is calculator without set-up?
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Paper 2 expects the standardisation or normCdf set-up shown explicitly, with the calculator-derived value at the end. A bare number loses marks.
What is q1?
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For X∼N(100,152)X \sim N(100, 15^2), use the empirical rule to estimate P(85≤X≤115)P(85 \le X \le 115). [2 marks]
What is q2?
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For X∼N(20,22)X \sim N(20, 2^2), find P(X≤23)P(X \le 23) by standardising. [3 marks]
What is q3?
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Scores are N(50,82)N(50, 8^2). Find the score exceeded by only the top 10%10\%. [3 marks]

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