About This Chapter
Who's It For?
Anyone who needs help learning or mastering the normal curve or continuous probability material will benefit from the lessons in this chapter. There is no faster or easier way to learn the normal curve and continuous probability distributions. Among those who would benefit are:
- Students who have fallen behind in understanding probability distributions
- 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 the normal curve and 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 normal curve and 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 normal curve and continuous probability distributions chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any normal curve or 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 normal curve and continuous probability distributions unit of a standard contemporary math course. Topics covered include:
- Graphing & developing probability distributions
- Finding the expected value of continuous random variables
- Continuous probability distribution
- Probabilities as geometric region areas
- Finding Z-scores
- Area estimation
- Estimating population percentages
- Normal distribution
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.
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Other chapters within the Contemporary Math: Help and Review course
- Mathematical Reasoning & Problem-Solving: Help and Review
- How to Solve Word Problems: Help and Review
- Statistics Overview: Help and Review
- Probability Overview: Help and Review
- Understanding Discrete Probability Distributions: Help and Review
- The Mathematics of Voting: Help and Review
- The Mathematics of Apportionment: Help and Review
- Graph Theory: Help and Review
- Operations with Basic Algebraic Expressions
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Performing Basic Arithmetic
- Operations with Monomials and Polynomials
- Number Line & the Coordinate Graph