Chapter 5 examines the normal distribution, its relationship to z-scores, and its applicability to probability theory and statistical inference. z-scores or standardized scores are values depicting how far a particular score is from the mean in standard deviation units. Different proportions of the normal curve area are associated with z-scores. The conversions of raw scores to z-scores and z-scores to raw scores are illustrated. Nonnormal distributions which differ markedly from normal curve characteristics are also described. The importance of the normal curve as a probability distribution, along with a brief introduction to probability, is discussed.

The final chapter of the textbook covers logistic regression, a statistical test used when the dependent variable is dichotomous or binary.OLS regression should not be used when the dependent variable is binary.The first discussion focuses on the limitations of OLS in this situation.The logit equation is presented and then steps for conducting a logistic regression in the R Commander are explained.Interpretation of the logistic regression output using odds ratios, percent change in odds, and predicted probabilities is discussed.Applied examples are used to better illustrate when to use logistic regression.

Uncertainty is a part of everyday life. We live with a range of situations that inherently have an element of uncertainty in them – for example, crossing the road, going on holiday, or making a major purchase – but we often ignore the embedded chance in these activities. Risk is acknowledged in many activities, and much effort is expended in identifying these risks and minimising any potential negative outcomes. In schools, for example, a risk assessment is required prior to any excursion with children. Probability is the strand of mathematics that addresses uncertainty. This chapter explores ideas relating to probability in the mathematics classroom.