ACMMM167
understand the effects of linear changes of scale and origin on the mean and the standard deviation.
ACMMM167 | 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
ACMMM141
recognise the variance and standard deviation of a discrete random variable as a measures of spread, and evaluate them in simple cases
ACMMM141 | Content Descriptions | Unit 3 | Mathematical Methods | Mathematics | Senior secondary curriculum
ACMMM166
recognise the expected value, variance and standard deviation of a continuous random variable and evaluate them in simple cases
ACMMM166 | Content Descriptions | Unit 4 | Mathematical Methods | Mathematics | Senior secondary curriculum
Links to Foundation to Year 10 Mathematical Methods
In Mathematical Methods, there is a strong emphasis on mutually reinforcing proficiencies in Understanding, Fluency, Problem solving and Reasoning. Students gain fluency in a variety of mathematical and statistical skills, including algebraic manipulations, …
Links to Foundation to Year 10 | 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
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
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