Using the Normal Distribution

Abstract

The normal distribution is the best-known of the statistical distributions. It results in the familiar “bell-shaped” or Gaussian curve. In this chapter, we shall develop a relationship between the Gaussian distribution and the mean and standard deviation treated earlier. Once we know the population mean and standard deviation of a randomly distributed continuous variable, we can predict the probability that future measurements will fall within any arbitrarily defined interval of the range of all possible measurements. We can also make statistical judgments whether any individual measurement or observation belongs to the set with a given mean and standard deviation or whether it belongs to some other set. These judgments rely on integration of the Gaussian function. In this book, of course, we do our integration by computer, a technique that is discussed at some length near the end of the chapter.