# Ch 9: Sampling Distributions in Statistics

### About This Chapter

## Sampling Distributions in Statistics - Chapter Summary and Learning Objectives

The short lessons in this chapter teach you all the methods for finding and using probabilities, including the steps needed to find z-scores, estimate population percentages and use normal distribution. Lessons use graphics and animations to make it easier for you to understand these concepts and entertain you in the process. You'll find plenty of examples and opportunities to practice the skills you're learning in these fast videos that take about 5-6 minutes to watch. By the end of the chapter, you'll be familiar with:

- The characteristics of normal distribution
- Methods for estimating areas under the normal curve
- Uses for the law of large numbers
- Ways to find mean and standard error of a sampling distribution

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

Normal Distribution: Definition, Properties, Characteristics & Example | Get a clear understanding of the properties and characteristics of normal distribution. |

Finding Z-Scores: Definition & Examples | Use the examples provided to learn how to find z-scores. |

Estimating Areas Under the Normal Curve Using Z-Scores | Armed with your knowledge of z-scores, use them to estimate areas under the normal curve. |

Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples | See how the empirical rule and normal distribution are used to estimate population percentages. |

Using the Normal Distribution: Practice Problems | Apply your skills from the previous lesson to practice problems that involve the normal distribution. |

How to Apply Continuous Probability Concepts to Problem Solving | Evaluate methods for solving problems that employ continuous probability. |

Understanding the Law of Large Numbers | Study the uses for this law and learn how it works. |

Sampling Distributions & The Central Limit Theorem: Definition, Formula & Examples | See the formula for the central limit theorem and find out where sampling distributions are used. |

Find the Mean & Standard Error of the Sampling Distribution | Figure out the steps needed to find a sampling distribution's mean and standard error. |

Finding Probabilities About Means Using The Central Limit Theorem | Determine how to use the central limit theorem to find probabilities about means. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. Sampling Distributions & the Central Limit Theorem: Definition, Formula & Examples

Want proof that all of this normal distribution talk actually makes sense? Then you've come to the right place. In this lesson, we look at sampling distributions and the idea of the central limit theorem, a basic component of statistics.

### 8. Find the Mean & Standard Error of the Sampling Distribution

Have you ever had a situation where one grade destroyed your average? Wouldn't you like a way of proving that your work was actually pretty good with that one exception? The standard error gives you such a chance.

### 9. Finding Probabilities About Means Using the Central Limit Theorem

The central limit theorem provides us with a very powerful approach for solving problems involving large amount of data. In this lesson, we'll explore how this is done as well as conditions that make this theorem valid.

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### Other Chapters

Other chapters within the DSST Principles of Statistics: Study Guide & Test Prep course

- Data Types & Measurements in Statistics
- Sampling Methods in Statistics
- Descriptive Statistics of Data Sets
- Visual Representations in Statistics
- Probability: Rules for Events
- Probability Combinations, Permutations & Expected Values
- Probability: Discrete & Continuous Distributions
- Correlation & Regression in Statistics
- Hypothesis Testing in Inferential Statistics
- DSST Informational Resources
- DSST Principles of Statistics Flashcards