11–12Mathematics Extension 1 11–12 Syllabus

Define a Bernoulli random variable as a model for two-outcome situations, referred to as success and failure

Define a Bernoulli distribution as the discrete probability distribution of a Bernoulli random variable

Identify contexts suitable to be modelled by Bernoulli random variables

Solve practical problems involving Bernoulli random variables

Identify contexts suitable to be modelled using binomial distributions

Define a binomial experiment as a fixed number of Bernoulli trials

Solve practical problems involving binomial distributions and binomial probabilities with and without online computational applications, excluding the normal approximation to the binomial distribution

Define a statistical population as the entire group of people or objects about which information is sought

Define a sample as a selection of people or objects drawn from a population

Recognise that, in general, the distribution of a population and a statistic, such as its mean, are unknown

Recognise that the sample means obtained from repeated sampling may be different, even if all the samples are of the same size

Recognise the significance of the central limit theorem for populations that are not necessarily normally distributed; that, irrespective of the population distribution, for a sufficiently large sample size, the sampling distribution of the mean is approximately normal

Examine the effect of the sample size on the variance of sample means with digital tools

Apply the central limit theorem to estimate the probability that the sample mean lies within given bounds