# CHAPTER 3

# Basic Concepts in Statistics and Probability

In this chapter we present the tools that form the foundation for the control charts that are covered in Part II and the other statistical procedures that are presented in Part III.

Much of the material in this chapter is typically found in introductory statistics texts. Some of the material is moderately advanced, so the reader may wish to use this chapter as reference material and read certain sections as needed.

## 3.1 PROBABILITY

During a typical day many of us will hear statements that are probability-type statements, although the word “probability” might not be used. One example (Statement 1) is a weather forecast in which a meteorologist states, “There is a 10% chance of rain tomorrow.” What does such a statement actually mean? For one thing, it means that, in the opinion of the meteorologist, it is very unlikely that rain will fall tomorrow. Contrast that with the following statement (Statement 2): “If a balanced coin is tossed, there is a 50% chance that a head will be observed.” Disregarding for the moment that the coin could land on its edge (an unlikely possibility), there are two possible outcomes, a head or a tail, and they are equally likely to occur. Finally, consider the following statement (Statement 3): “I found a slightly bent coin in the street. I am going to toss this coin 1000 times and use the results of this experiment to determine an estimate of the likelihood of obtaining a head when the coin is tossed ...