## ABSTRACT

Chapter 5 expands the discussion on probability distribution functions to include continuous random variables. The general normal distribution and standard normal distribution are introduced in this chapter. The normal distribution is a foundational distribution used in biostatical theory. Several other key concepts and methods used for statistical analysis that are covered in subsequent chapters of this book (e.g., confidence intervals, hypothesis testing, and linear regression) are based on the normal distribution. The example and practice problems in Chapter 5 allow readers to find probabilities using the standard normal curve given a population mean and standard deviation, and the problems allow readers to address public health problems that lend themselves to a probabilistic framework. Users learn how to read the standard normal table (Appendix Table A.3) and how to use statistical software (SAS and Stata) to calculate probabilities and find cutoffs for the standard normal distribution. The relationships among the binomial, Poisson, and normal distributions are explained with assumptions for when each can be used to approximate the others.