# Ch 6: Continuous Probability Distributions: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering college statistics material will benefit from taking this course. There is no faster or easier way to learn college statistics. Among those who would benefit are:

- Students who have fallen behind in understanding probabilities as areas of geometric regions or working with normal distribution
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about continuous probability distributions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Continuous Probability Distributions chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Continuous Probability Distributions chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any continuous probability distributions question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a Continuous Probability Distributions unit of a standard college statistics course. Topics covered include:

- Graphing probability distributions associated with random variables
- Finding and interpreting the expected value of a continuous random variable
- Normal distribution
- Finding Z-scores
- Applying continuous probability concepts to problem solving

### 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.

### 10. Using Normal Distribution to Approximate Binomial Probabilities

Binomial probabilities describe processes in our world. Learn how to create and interpret a binomial probability distribution graph, and discover how the normal distribution can form a good approximation of the binomial distribution.

### 11. How to Apply Continuous Probability Concepts to Problem Solving

Continuous probability distributions can be a good approximation of many real world processes and phenomena. In this lesson, you will gain a conceptual understanding of continuous probability distributions and how to apply their properties to solve problems.

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### Other Chapters

Other chapters within the Introduction to Statistics: Help and Review course