ACMMM168
identify contexts such as naturally occurring variation that are suitable for modelling by normal random variables
ACMMM168 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM169
recognise features of the graph of the probability density function of the normal distribution with mean \(\mu\) and standard deviation \(\sigma\) and the use of the standard normal distribution
ACMMM169 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM170
calculate probabilities and quantiles associated with a given normal distribution using technology, and use these to solve practical problems.
ACMMM170 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM171
understand the concept of a random sample
ACMMM171 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM172
discuss sources of bias in samples, and procedures to ensure randomness
ACMMM172 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM173
use graphical displays of simulated data to investigate the variability of random samples from various types of distributions, including uniform, normal and Bernoulli.
ACMMM173 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM174
understand the concept of the sample proportion \(\widehat p\) as a random variable whose value varies between samples, and the formulas for the mean \(p\) and standard deviation \(\sqrt[{}]{(p(1-p)/n}\) of the sample proportion \(\widehat p\)
ACMMM174 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM175
examine the approximate normality of the distribution of \(\widehat p\) for large samples
ACMMM175 | 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
ACMMM177
the concept of an interval estimate for a parameter associated with a random variable
ACMMM177 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM178
use the approximate confidence interval \(\left(\widehat p-z\sqrt[{}]{(\widehat p(1-\widehat p)/n},\;\;\widehat p+z\sqrt[{}]{(\widehat p(1-\widehat p)/n}\right),\) as an interval estimate for \(p\), where \(z\) is the appropriate quantile for the standard …
ACMMM178 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
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
ACMMM180
use simulation to illustrate variations in confidence intervals between samples and to show that most but not all confidence intervals contain \(p\)
ACMMM180 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMSM001
solve problems involving permutations
ACMSM001 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM002
use the multiplication principle
ACMSM002 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM003
use factorial notation
ACMSM003 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM004
solve problems involving permutations and restrictions with or without repeated objects
ACMSM004 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM005
determine and use the formulas for finding the number of elements in the union of two and the union of three sets.
ACMSM005 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM006
solve problems and prove results using the pigeon-hole principle.
ACMSM006 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum
ACMSM007
solve problems involving combinations
ACMSM007 | Content Descriptions | Unit 1 | Specialist Mathematics | Mathematics | Senior secondary curriculum