# Chapter 9: The Normal Distribution

**At Grade**Created by: CK-12

The normal distribution can be found practically everywhere, from the distribution of human heights to IQ scores. Understanding the application of the normal distribution can simplify the calculation of binomial probabilities, such as the probability of flipping heads 37 or more times out of 60. By using the Central Limit Theorem, you can evaluate the probabilities associated with many different random variables.

## Chapter Outline

- 9.1. Understanding Normal Distribution
- 9.2. The Empirical Rule
- 9.3. Z-Scores
- 9.4. Z Scores II
- 9.5. Z-scores III
- 9.6. The Mean of Means
- 9.7. Central Limit Theorem
- 9.8. Approximating the Binomial Distribution

### Chapter Summary

Students practiced the application of the normal distribution, and were introduced to the Empirical rule and the concept and calculation of *z*-scores. *Z*-score probabilities were introduced, and students practiced associating *z*-scores with probabilities via reference tables and technology. The concept of the sampling distribution of the sample mean was introduced, along with the Central Limit Theorem. Finally, students practiced using the normal distribution to approximate the output of binomial random variables.