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- 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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