### Unit 3: The Normal Distribution

A distribution is a line graph representation of the probability that an event will occur. It is similar to a histogram, but in a distribution, the user does not determine the grouping; instead, data is grouped according to the likelihood that it will occur within the data set. Distributions also allow for analysis of a specific event, whereas a histogram requires events be grouped.

An important type of this distribution is the "normal" distribution. The normal distribution is used to approximate real-world occurrences. If you can make certain assumptions about the occurrence of an event, then you can use the normal distribution to find out the probabilities of that event occurring. Many of the events that are important to business can be approximated using the normal distribution.

**Completing this unit should take you approximately 3 hours.**

Upon successful completion of this unit, you will be able to:

- define and apply the properties of the normal distribution while understanding real-world implications and applications of the normal distribution;
- use the normal distribution to estimate the probability of an event occurring; and
- explain how the normal distribution relates to the central limit theorem.

- define and apply the properties of the normal distribution while understanding real-world implications and applications of the normal distribution;

### 3.1: The Normal Distribution

Watch this video, which gives an intuitive explanation of variables in real life that follow a normal distribution.

Read this chapter, which covers some of the most important concepts used in statistics: the central limit theorem and the normal distribution. Make sure you read the introduction and sections 7.1 through 7.4. Attempt the practice problems and homework at the end of the chapter, which will give you a chance to check your understanding of these concepts.

Watch this video, which will walk you through the process of finding Z-scores, an important part of understanding this topic.

Watch this video, will walk you through the process of solving problems using the standard normal distribution, an important part of understanding this topic.

### Unit 3 Problem Set and Assessment

Complete all five exercises. You can check your work by clicking "Show Solution".

Take this assessment to see how well you understood this unit.

- This assessment
**does not count towards your grade**. It is just for practice! - You will see the correct answers when you submit your answers. Use this to help you study for the final exam!
- You can take this assessment as many times as you want, whenever you want.

- This assessment