# Ch 6: Continuous Probability Distributions: Tutoring Solution

### About This Chapter

## How it works:

- Begin your assignment or other statistics work.
- Identify the continuous probability distributions concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our statistics tutoring solution will benefit any student who is trying to learn about continuous probability distributions and earn better grades. This resource can help students including those who:

- Struggle with normal distributions, random variables, Z-scores or any other continuous probability distributions topic
- Have limited time for studying
- Want a cost effective way to supplement their statistics learning
- Prefer learning statistics visually
- Find themselves failing or close to failing their continuous probability distributions unit
- Cope with ADD or ADHD
- Want to get ahead in statistics
- Don't have access to their statistics teacher outside of class

## Why it works:

**Engaging Tutors**: We make learning continuous probability distributions simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live statistics tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about continuous probability distributions on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Graph probability distributions.
- Find expected values of continuous random variables.
- Develop continuous probability distributions theoretically.
- Understand probabilities as geometric areas.
- Name the characteristics of normal distribution.
- Learn how to find z-scores.
- Use z-scores to calculate the areas under the normal curve.
- Use normal distributions and the empirical rule to estimate population percentages.
- Approximate binomial probabilities using normal distribution.
- Describe the appropriate applications of continuous probability concepts.

### 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: Tutoring Solution course