# Experience 8 - The Central Limit Theorem

**The Central Limit Theorem**

**Why**

The central limit theorem is the most important result in elementary statistics. It will allow us to take any population - skewed, uniform, bi-modal, etc. and convert it to a problem with a normal distribution, provided the samples are random and the sample size is large enough. Once we have a normal distribution we can use all the techniques of experience 7 to determine anything we want to know about it. This chapter thus serves as our justification for the process used in the next four experiences.

**Learning Objectives**

- Understand what a sampling distribution is
- Know the requirements of the central limit theorem
- Know the consequences of the central limit theorem

**Performance Criteria**

- The learner will observe the creation of sampling distributions using simulations.
- The learner will verify that requirements for the central limit theorem are met when solving problems.
- The learner will calculate the mean and standard deviation for sampling distributions for the mean.

**Videos**

Chapter 7 (This is a video by the authors covering chapter 7. Just watch the parts relating to section 7.1)

Calculating Probabilities for a Sampling Distributions (TI-84)

Calculating Probabilities for a Sampling Distributions (Excel)

Use this site to simulate the creation of sampling distributions.

Click on "Textbook" to view the reading assignment for this experience or read section 7.1 from your print or digital copy.

**Plan**

- Review - Read the above components and post any questions in the forum below.
- Practice - Complete the practice exercises that follow.
- Think - Answer the Critical Thinking questions in the "Critical Thinking" forum.
- Apply - Complete the Application Problems and upload your completed files.

If you have any questions about the content (readings, problems, etc.) then post in the "Questions about Experience 8" forum.

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