Chapter 5The Normal Distribution

Only a textbook in statistics could get away with entitling a chapter “The Normal Distribution.” If you thought that the topic of distributions was less than exciting, then what chance does a normal one have? No matter how hard you try you cannot get away from the normal distribution. Every time you see the results of a political poll in the news, those results are based on the normal distribution. The findings from most scientific studies – from those telling you that you need more exercise to those bragging their batteries last the longest – all rely on the normal distribution. In this chapter, we will consider attributes of datasets that are distributed normally. While it is true that some data are naturally known to be normally distributed, the real usefulness of the normal distribution starts in Chapter 6 on sampling distributions. However, before we get there, we need to know the fundamentals, and introducing those fundamentals is the goal of this chapter. The normal distribution is a continuous probability distribution, implying that the underlying data are continuous. Recall, continuous data can take on any value within a range (i.e., fractions make sense). As we will find out later, however, sometimes even discrete data can be safely approximated as normal.

5.1 The Bell Shape

The normal distribution is probably best described as a “bell-shaped” distribution. Some textbooks call it “mound shaped.” Fancier textbooks call it “Gaussian”, ...

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