ABSTRACT
We introduce continuous probability distributions, beginning with the normal or Gaussian distribution, also called the bell curve. We show how two parameters, the mean and standard deviation, are used to ascertain probabilities of ranges of values of variables that have a normal distribution, including the use of the standard normal distribution. We explain the concept and use of sampling distributions to model the variation of sample statistics, focussing on the sample mean, and emphasise the role of the standard error, its relationship with sample size and basis in the central limit theorem. We differentiate between the population standard deviation and the sample standard deviation and explain how the latter is used to approximate the former. We introduce Student’s t distribution and clarify when to use it instead of the normal distribution in modelling sampling distributions for small samples.
