The Normal Distribution

Summary :

This chapter presents the normal distribution as the most important of all continuous distributions, appearing across psychology, business, economics, and the sciences, while cautioning that it cannot be applied to everything. It covers the distribution's two parameters, the standard normal distribution, and how to use the normal distribution to find probabilities.

The most important, and most abused, distribution

The chapter opens by calling the normal distribution the most important of all distributions, noting its bell-shaped graph appears across psychology, business, economics, and the sciences and that some instructors even use it to help set grade curves, while explicitly cautioning that it is also widely misapplied and cannot be assumed for every real-world quantity.

Two parameters and the standard normal distribution

A normal distribution is fully described by two numerical parameters, its mean μ and its standard deviation σ, and the chapter introduces the standard normal distribution, the special case with mean zero and standard deviation one, as the reference distribution used to compute probabilities for any normal distribution by converting, or standardizing, values onto it.

Using the normal distribution

Once a quantity is established as normally distributed with a given mean and standard deviation, the chapter shows how to use the distribution to find probabilities for specified ranges of values, representing them as shaded areas under the bell curve, building the practical skill of moving between raw values and the probabilities they correspond to.