The Normal Distribution

Summary :

This chapter uses the example of shoe sizes forming a bell curve to introduce the normal distribution, noting it is used, and sometimes abused, across psychology, business, economics, and the sciences. It covers recognizing and applying the normal probability distribution, the standard normal distribution, and converting between the two to compare probabilities.

A bell curve across many fields

The chapter introduces the normal distribution through the example of shoe sizes graphing into a bell-shaped curve, noting that the same pattern appears across psychology, business, economics, and the sciences, and that some instructors even use it to help set grades, while emphasizing that recognizing when it does and does not apply is itself a skill.

The standard normal distribution

Students learn to recognize and apply the standard normal probability distribution appropriately, the reference version of the normal distribution used to standardize any normally distributed value so that probabilities can be looked up or computed consistently regardless of the original mean and standard deviation.

Comparing probabilities across distributions

The chapter covers comparing normal probabilities by converting values to the standard normal distribution, a technique that lets students compare two values from different normal distributions, such as scores on two different tests, on a common scale before drawing any conclusion about which is relatively higher or lower.