# Ch 55: PLACE Mathematics: Continuous Probability Distributions

### About This Chapter

## PLACE Mathematics: Continuous Probability Distributions - Chapter Summary

Let us give you a fast and easy way to brush up on and master the concepts of continuous probability distribution that you may encounter on the PLACE Mathematics exam. Our fun video lessons cover the topics you'll need to know, including:

- Graphing probability distributions with random variables
- Interpreting the expected value of a continuous random variable
- Theoretically developing continuous probability distributions and finding expected values
- Properties of normal distribution
- Estimating population percentages from normal distributions using the empirical rule
- Approximating binomial probabilities from normal distribution

Expert instructors lead you through each lesson, and you can read along with the transcripts as well. The lessons are designed to be viewed on a computer or mobile device, making it easy for you to study whenever you have time.

### Objectives of the PLACE Mathematics: Continuous Probability Distributions Chapter

The exam will test your knowledge of multiple math concepts, such as probability distributions and their applications. The topics you'll study in this chapter can be found in the Statistics and Probability part of the exam, which constitutes 19% of the whole test.

The exam questions are all multiple-choice and require you to select the correct answer. Use our practice quizzes at the end of each lesson to get familiar with the types of questions you'll see.

### 1. Graphing Probability Distributions Associated with Random Variables

Even if they may feel rigged, games of luck like playing the lottery or slot machines in a casino are random in nature. In this lesson, learn the definition of a random variable and how to graph probability distributions associated with them.

### 2. Finding & Interpreting the Expected Value of a Continuous Random Variable

A continuous random variable deals with measurements with an infinite number of likely outcomes. Define random variables and learn how to compute and to interpret the expected value of a continuous random variable with the probability density function.

### 3. Developing Continuous Probability Distributions Theoretically & Finding Expected Values

In math, random variables can be defined using the probability distribution function. Learn about the types of random processes and variables, continuous probability distribution, and how to find expected values.

### 4. Normal Distribution: Definition, Properties, Characteristics & Example

A normal distribution is a probability distribution characterized by a bell-shaped curve. Learn about the definition, properties, characteristics, and examples of normal distribution, and discover the empirical rule for normally distributed data.

### 5. Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples

In statistics, the number of standard deviations something is away from its normal distribution is called the z-score. Learn more about the z-score and normal distribution with respect to the empirical rule and how to use it to estimate population percentages.

### 6. Using Normal Distribution to Approximate Binomial Probabilities

Binomial probabilities show the possibility that in multiple tests with only two potential outcomes, the same result will occur. Learn about using normal distribution to approximate binomial probabilities, explore calculating odds, define binomial probabilities, and understand how to approximate binomial distributions and relate them to normal distributions.

### Earning College Credit

Did you know… We have over 220 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Other Chapters

Other chapters within the PLACE Mathematics: Practice & Study Guide course

- PLACE Mathematics: Properties of Real Numbers
- PLACE Mathematics: Fractions
- PLACE Mathematics: Decimals & Percents
- PLACE Mathematics: Ratios & Proportions
- PLACE Mathematics: Measurements & Conversions
- PLACE Mathematics: Logic
- PLACE Mathematics: Mathematical Reasoning
- PLACE Mathematics: Vector Operations
- PLACE Mathematics: Matrices & Determinants
- PLACE Mathematics: Exponents & Exponential Expressions
- PLACE Mathematics: Algebraic Expressions
- PLACE Mathematics: Linear Equations
- PLACE Mathematics: Inequalities
- PLACE Mathematics: Absolute Value Problems
- PLACE Mathematics: Quadratic Equations
- PLACE Mathematics: Polynomials
- PLACE Mathematics: Rational Expressions
- PLACE Mathematics: Radical Expressions
- PLACE Mathematics: Systems of Equations
- PLACE Mathematics: Complex Numbers
- PLACE Mathematics: Functions
- PLACE Mathematics: Graphing Piecewise Functions
- PLACE Mathematics: Exponential and Logarithmic Functions
- PLACE Mathematics: Continuity of Functions
- PLACE Mathematics: Limits
- PLACE Mathematics: Rate of Change
- PLACE Mathematics: Calculating Derivatives & Derivative Rules
- PLACE Mathematics: Graphing Derivatives & L'Hopital's Rule
- PLACE Mathematics: Applications of Derivatives
- PLACE Mathematics: Area Under the Curve & Integrals
- PLACE Mathematics: Integration & Integration Techniques
- PLACE Mathematics: Integration Applications
- PLACE Mathematics: Foundations of Geometry
- PLACE Mathematics: Introduction to Geometric Figures
- PLACE Mathematics: Properties of Triangles
- PLACE Mathematics: Triangles, Theorems & Proofs
- PLACE Mathematics: Parallel Lines & Polygons
- PLACE Mathematics: Quadrilaterals
- PLACE Mathematics: Circular Arcs & Circles
- PLACE Mathematics: Conic Sections
- PLACE Mathematics: Geometric Solids
- PLACE Mathematics: Analytical Geometry
- PLACE Mathematics: Using Trigonometric Functions
- PLACE Mathematics: Trigonometric Graphs
- PLACE Mathematics: Solving Trigonometric Equations
- PLACE Mathematics: Trigonometric Identities
- PLACE Mathematics: Sequences & Series
- PLACE Mathematics: Graph Theory
- PLACE Mathematics: Set Theory
- PLACE Mathematics: Overview of Statistics
- PLACE Mathematics: Summarizing Data
- PLACE Mathematics: Tables & Plots
- PLACE Mathematics: Probability
- PLACE Mathematics: Discrete Probability Distributions
- PLACE Mathematics: Sampling
- PLACE Mathematics: Hypothesis Testing
- PLACE Mathematics: Regression & Correlation
- PLACE Mathematics Flashcards