About This Chapter
Distribution & Inference in Statistics - Chapter Summary
Instructors begin this chapter on normal distribution by examining its properties. You can take a look at this bell curve's symmetrical center and single mode, as well as the asymptotes at either end, and learn how the normal distribution is used to estimate population percentages.
The relationship between normal distributions, standard deviations and z-scores is covered as well. Video lessons show you the processes involved in finding these measures and illustrate the uses of z-scores to estimate areas.
The chapter concludes with lessons relating normal distribution to two main probability theorems, the central limit theorem and the law of large numbers, both of which can be used to describe the sampling distributions and expected values of an experiment's outcomes. By the time you finish these lessons, you should be familiar with the following:
- Characteristics of normal distribution
- The steps for finding and using z-scores
- Applications of the law of large numbers
- Uses of the central limit theorem
This chapter contains plenty of resources to help you master the concept of normal distribution. In addition to illustrated videos taught by experienced instructors, there are transcripts with embedded links to text lessons that outline key statistics terminology. Lessons also include practice problems, as well as self-assessment quizzes, to help ensure you've got a firm grasp of the main ideas.
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. 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.
3. Binomial Distribution: Definition, Formula & Examples
You have a probability distribution to create, which one do you use? That depends. In this lesson, learn about binomial distributions, get examples and criteria for their use, and learn how to calculate the binomial distribution formula.
4. Understanding the Law of Large Numbers
The law of large numbers is a concept that is often misunderstood in statistics. In this lesson, you will learn the real meaning of the law of large numbers and how it is employed.
5. 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.
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Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Mathematical Process & Perspectives
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards