Continuous Random Variables

In chapter 5 we began the study of probability, needed for inference in the process of statistics. In chapter 6 we studied distributions that arise for discrete random variables. We spent most of our time working with the binomial distribution, although there are others that exist that can be looked up in other books. We discovered ways to describe the distributions in terms of center, variation, and shape.

In chapter 7 we will study continuous random variables. One continuous distribution that is of special importance is the normal distribution, which is another name for a perfectly bell-shaped curve. Again, there are others, but we will focus on the normal distribution because it has so many uses.

The process of statistics

By the end of this chapter, you will be able to:

•identify and interpret discrete and continuous random variables.

•identify a continuous probability distribution.

•describe the standard normal and non-standard normal distributions.

•find probability as an area from a normal distribution.

•find and interpret percentiles from a normal distribution.

•describe and apply the central limit theorem.

•describe sampling distributions for the mean.

•find probability relating to the sampling distribution of the mean.

•describe the distribution of sample proportions.

•find probability relating to the sampling distribution of the sample proportion.