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QLDMath MethodsQuick questions
Unit 4: Further calculus and statistical inference
Quick questions on The normal distribution and standardisation: QCE Maths 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 paper 1?Show answer
When the endpoints map cleanly to $\mu \pm n \sigma$ for $n = 1, 2, 3$, use the empirical rule.
What is quality control?Show answer
Lengths or weights of manufactured items modelled as normal.
What is test scores?Show answer
Standardised test scores have a bell-curve distribution.
What is biological measurements?Show answer
Heights, blood pressure, gestation periods.
What is modelling errors?Show answer
Random measurement errors typically follow a normal distribution.
What is paper 1 empirical-rule?Show answer
Find $P(160 \leq X \leq 240)$.
What is paper 2 inverse?Show answer
Find $c$ such that the longest 10 percent of batteries are warranted to last more than $c$ hours.
What is wrong sign on standardisation?Show answer
$z = (x - \mu)/\sigma$, not $(\mu - x)/\sigma$.
What is empirical rule misapplied?Show answer
The rule is for $\mu \pm n \sigma$ specifically. For other endpoints, standardise and use a table or calculator.
What is inverse for the wrong tail?Show answer
"Top 10 percent" means $P(X > c) = 0.10$, so $P(X \leq c) = 0.90$. Read carefully.
What is using $\sigma^2$ where $\sigma$ is asked?Show answer
$z = (x - \mu)/\sigma$ uses the standard deviation, not the variance.
What is calculator without set-up?Show answer
Paper 2 expects the standardisation set-up shown explicitly with the calculator value at the end.