# Ch 6: The Normal Curve & Continuous Probability Distributions

### About This Chapter

## The Normal Curve and Continuous Probability Distributions - Chapter Summary and Learning Objectives

The normal curve, also commonly known as the bell curve, describes the mathematical concept of normal distribution. This means that most of the data is concentrated in the middle of the curve and that it is uncommon for data points to fall at either extreme end of the curve. Normal distribution is an example of a continuous probability distribution. The lessons in this chapter will teach you all about the characteristics of normal distributions and how to use them to determine probabilities. This chapter is designed to teach you how to:

- Graph probability distributions
- Find z-scores
- Find expected values of continuous random variables
- Estimate areas under the normal curve
- Use normal distributions to estimate population percentages

Video | Objective |
---|---|

Graphing Probability Distributions Associated with Random Variables | Represent probability distributions graphically |

Finding & Interpreting the Expected Value of a Continuous Random Variable | Find expected values of continuous random variables |

Developing Continuous Probability Distributions Theoretically & Finding Expected Values | Use probability theory to develop continuous probability distributions |

Probabilities as Areas of Geometric Regions: Definition & Examples | Conceptualize probabilities as geometric areas |

Normal Distribution: Definition, Properties, Characteristics & Example | Describe the properties and characteristics of normal distribution |

Finding Z-Scores: Definition & Examples | Determine z-scores |

Estimating Areas Under the Normal Curve Using Z-Scores | Use z-scores to find areas under the normal curve |

Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples | Use the empirical rule and normal distributions to estimate population percentages |

Using the Normal Distribution: Practice Problems | Use normal distribution to find probabilities |

### 1. Graphing Probability Distributions Associated with Random Variables

What's a random variable? Does it have anything to do with gambling? What's the difference between a continuous and a discrete variable? This lesson explains the difference and how to graph each one.

### 2. Finding & Interpreting the Expected Value of a Continuous Random Variable

How can you find the expected value of something like height distributions? This lesson explains how to find and interpret the expected value of a continuous random variable.

### 3. Developing Continuous Probability Distributions Theoretically & Finding Expected Values

What is an expected value? How can you tell how many time you should expect a coin to land on heads out of several flips? This lesson will show you the answers to both questions!

### 4. Probabilities as Areas of Geometric Regions: Definition & Examples

In this lesson, you're going to learn what a random variable is and examine core concepts related to probabilities as areas of geometric regions and expected values of probability distributions.

### 5. Normal Distribution: Definition, Properties, Characteristics & Example

In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.

### 6. Finding Z-Scores: Definition & Examples

Talking about multiples of standard deviations can get exhausting and confusing. Luckily, z-scores allow us to talk about how far a point is removed from a mean in terms of how many standard deviations away it is.

### 7. Estimating Areas Under the Normal Curve Using Z-Scores

So now that we have a Z-score, what is it used for? Sure, it can make your life easier when describing standard deviations, but finding the area under the normal curve is where the Z-score shines.

### 8. Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples

If you've been working with z-scores for long, you probably get tired of checking those tables every time you need to check the area under the curve. Luckily, the empirical rule helps us memorize the most important values.

### 9. Using the Normal Distribution: Practice Problems

In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. Review the concepts with a short quiz at the end.

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Math 106: Contemporary Math course