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VICMath MethodsQuick questions
Unit 4
Quick questions on The normal distribution: VCE Math Methods Unit 4
12short 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 worked standardisation?Show answer
$X \sim N(50, 4^2)$. Find $P(X \leq 56)$.
What is worked inverse normal?Show answer
$X \sim N(50, 0.4^2)$. Find $c$ such that $P(X > c) = 0.10$.
What is quality control?Show answer
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?Show answer
Scores on standardised tests are typically modelled as normal.
What is biology and medicine?Show answer
Heights, blood pressure, gestation periods, biomarker levels are often approximately normal.
What is finance?Show answer
Returns on a portfolio over a fixed period are sometimes modelled as normal (in basic Methods contexts; real finance uses heavier tails).
What is standardisation with the wrong denominator?Show answer
$z = (x - \mu) / \sigma$, not $(x - \mu) / \sigma^2$. Divide by the standard deviation, not the variance.
What is forgetting the standardisation when using $Z$-tables?Show answer
If you look up $z$ directly using $x$, you get the wrong probability.
What is inverse direction error?Show answer
"$P(X > c) = 0.10$" means $c$ is in the upper tail; "$P(X < c) = 0.10$" means $c$ is in the lower tail. Use $1 - p$ if needed before invNorm.
What is empirical rule misapplied?Show answer
The empirical rule is for $\mu \pm n\sigma$ specifically. For other endpoints, standardise and use a table or calculator.
What is using $\sigma^2$ where $\sigma$ is asked for?Show answer
The standard deviation is $\sigma$, not $\sigma^2$. Remember to take the square root if you computed variance.
What is calculator without set-up?Show answer
Paper 2 expects the standardisation or normCdf set-up shown explicitly, with the calculator-derived value at the end. A bare number loses marks.