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9. Continuous random variables
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AustraliaVIC
VCE 12 Methods 2023

9.05 Normal distributions

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Interactive practice questions

Which of these curves is normally distributed?

A

B

C
Easy
< 1min

Which of the following sets of data is approximately normally distributed?

Easy
< 1min

Which of these histograms is approximately normally distributed?

Easy
< 1min

Which of these box-and-whisker plots represents data that is normally distributed?

Easy
< 1min
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Outcomes

U34.AoS4.3

continuous random variables: - construction of probability density functions from non-negative functions of a real variable - specification of probability distributions for continuous random variables using probability density functions - calculation and interpretation of mean, 𝜇, variance, 𝜎^2, and standard deviation of a continuous random variable and their use - standard normal distribution, N(0, 1), and transformed normal distributions, N(𝜇, 𝜎^2), as examples of a probability distribution for a continuous random variable - effect of variation in the value(s) of defining parameters on the graph of a given probability density function for a continuous random variable - calculation of probabilities for intervals defined in terms of a random variable, including conditional probability (the cumulative distribution function may be used but is not required)

U34.AoS4.4

statistical inference, including definition and distribution of sample proportions, simulations and confidence intervals: - distinction between a population parameter and a sample statistic and the use of the sample statistic to estimate the population parameter - simulation of random sampling, for a variety of values of 𝑝 and a range of sample sizes, to illustrate the distribution of 𝑃^ and variations in confidence intervals between samples - concept of the sample proportion as a random variable whose value varies between samples, where 𝑋 is a binomial random variable which is associated with the number of items that have a particular characteristic and 𝑛 is the sample size - approximate normality of the distribution of P^ for large samples and, for such a situation, the mean 𝑝 (the population proportion) and standard deviation - determination and interpretation of, from a large sample, an approximate confidence interval for a population proportion where 𝑧 is the appropriate quantile for the standard normal distribution, in particular the 95% confidence interval as an example of such an interval where 𝑧 ≈ 1.96 (the term standard error may be used but is not required).

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