## Graphing Probability Distributions

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-MD.A.1

Tips For Graphing Probability Distributions - A function that can be used to obtain possible values for a random variable is termed as probability distribution. The value of variables depends on probability distribution. The function helps in describing probabilities. The sum of all probabilities is equal to one. The probability of a single event must always lie between the 0 and 1. There are different types of probability distributions including binomial, Chi-square, F-distribution, Normal, and student's t distribution. Probability distributions can be graphed, and the visual representation of the distribution helps in showing the features that were not visible in the data on paper. You must always place the random variable on the x-axis and plot its probability on the y-axis. Discrete random variables always use histograms while continuous random variable uses a smooth curve. The area of the curve helps in calculating the probability. A probability distribution graph will never include negative values on the y-axis. These worksheets and lessons help students learn how to graph of a probability distribution and also make sense of the visual display to others.

### Printable Worksheets And Lessons

- Working the Data Step-by-step Lesson- You are given pretty random data and you need to graph the distribution and comment on it.
- Guided Lesson - On the third problem we give you the characteristics of a normal curve and ask you to add it to the second graph.
- Guided Lesson Explanation - I just generated one graph for number three, it is all there though.
- Practice Worksheet - Three full out problems for you to work twice over.
- Matching Worksheet - This is just a quick introduction. It is very helpful because most national tests will just hit you with multiple choice questions similar to this.

#### Homework Sheets

It's all about drawing relative frequency histograms of the data.

- Homework 1 - We create a histogram using the values dictated by the table to the right. The relative frequency histogram is symmetric.
- Homework 2 - Focus on the symmetry of the histogram to make sense of it.
- Homework 3 - Compare the area of the rectangle for heights between 30 and 30.9 inches to the area under the normal curve for heights between 30 and 30.9 inches.

#### Practice Worksheets

Make sure to explain the shape of the data distribution.

- Practice 1 - Draw a relative frequency histogram of the data. Comment on the shape of the distribution.
- Practice 2 - A symmetric relative frequency histogram favors the middle value, just like a bell curve.
- Practice 3 - See if the normal curve is slightly above the point in question.

#### Math Skill Quizzes

Some of the work on quiz 3 is pretty difficult.