ACMMM179
define the approximate margin of error \(E=z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\) and understand the trade-off between margin of error and level of confidence
ACMMM179 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM176
simulate repeated random sampling, for a variety of values of \(p\) and a range of sample sizes, to illustrate the distribution of \(\widehat p\) and the approximate standard normality of \(\frac{\widehat p\;-p}{\sqrt[{}]{(\widehat p(1-\widehat p)/n}}\) …
ACMMM176 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM055
define and use basic linear transformations: dilations of the form \((\mathrm x,\mathrm y)\longrightarrow({\mathrm\lambda}_1\mathrm x,{\mathrm\lambda}_2\mathrm y)\) , rotations about the origin and reflection in a line which passes through the origin, …
ACMSM055 | Content Descriptions | Unit 2 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMMM045
use the notation \(\begin{pmatrix}n\\r\end{pmatrix}\) and the formula \(\begin{pmatrix}n\\r\end{pmatrix}=\frac{n!}{r!\left(n-r\right)!}\) for the number of combinations of \(r\) objects taken from a set of \(n\) distinct objects
ACMMM045 | Content Descriptions | Unit 1 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM149
determine and use the probabilities \(\mathrm P\left(\mathrm X=\mathrm r\right)=\begin{pmatrix}\mathrm n\\\mathrm r\end{pmatrix}\mathrm p^\mathrm r{(1-\mathrm p)}^{\mathrm n-\mathrm r}\) associated with the binomial distribution with parameters \(n\) …
ACMMM149 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum