INTRODUCTION TO PROBABILITY: THE BINOMIAL AND NORMAL PROBABILITY DISTRIBUTIONS
The theory of statistics is based on probability. Some basic definitions and theorems are introduced in this chapter. This elementary discussion leads to the concept of a probability distribution, a mathematical function that assigns probabilities for outcomes in its domain. The properties of (a) the binomial distribution, a discrete distribution, and (b) the normal distribution, a continuous distribution, are presented. The normal distribution is the basis of modern statistical theory and methodology. One of the chief reasons for the pervasion of the normal distribution in statistics is the central limit theorem, which shows that means of samples from virtually all probability distributions tend to be normal for large sample sizes. Also, many of the probability distributions used in statistical analyses are based on the normal distribution. These include the t, F, and Chi-square distributions. The binomial distribution is applicable to experimental results that have two possible outcomes, such as pass or fail in quality control, or cured or not cured in a clinical drug study. With a minimal understanding of probability, one can apply statistical methods intelligently to the simple but prevalent problems that crop up in the analysis of experimental data.