**Binomial Probability Distribution**

Purpose: The purpose of this assignment is to find the binomial probability of a certain experiment and then compare the results of the experiment to the predicted probability.

Experiment: A die is rolled 8 times and the number of times the die lands on a “5” is recorded.

Methods: Use a graphing calculator to find the binomial probabilities. Round the probabilities to 3 significant digits. Use Excel (or similar software) to create the tables. Then copy the items and paste them into a Word document. The tables should be formatted vertically, have borders, and be given the labels and titles stated in the assignment. The proper symbols should be used. Do not submit this assignment as an Excel file. The completed assignment should be a Word (or .pdf) document.

Part 1: The Binomial Probability Distribution

1. State the values of n and p. Define the random variable (what it represents, not a numerical value.)

2. Find the probability that 2 of the rolls will be a “5.”

3. Find the expected value of the binomial probability distribution.

4. The random variable has values between 0 and n (0 < x < n). Make a table to record the binomial probability of each value of the random variable. The left column will be for the random variable and will have values from 0 to n. The right column will have the probability of each of the values. The probabilities should be rounded to 3 significant digits. Label this “Table 1: Binomial Probability Distribution of the Experiment.”

Part 2: Conduct the Experiment

1. The sample data will be found by using an online simulator for rolling dice. The simulator rolls from 1 to 6 dice.

http://www.dicesimulator.com/

Set the simulator to roll 4 dice so that 2 rolls is the same as rolling a die 8 times. Record the number of dice that landed on a “5’.” Repeat the experiment 20 times, recording the number of “5’s” for each repetition. Use technology (Excel, graphing calculator, etc.) to sort the data from low to high. Use Excel or similar software to put the data into a table with 5 columns containing 4 values each. Label this “Table 2: Sorted Values of the Random Variable.”

2. The random variable has values between 0 and n (0 < x < n). Make a table to record the frequencies of each value of the random variable. The left column is for the random variable and will have values from 0 to n. The right column will have the frequencies of each of the values. Find the frequencies from Table 2. Label this “Table 3: Frequencies of Values of the Random Variable.”

3. Divide each of the frequencies in Table 3 by 20 to create a relative frequency distribution. Label this “Table 4: Relative Frequencies of Values of the Random Variable.” The relative frequencies should be rounded to 3 significant digits.

4. Find the relative frequency for the case of having 2 of the 8 rolls being a “5.”

5. Find the mean value of the relative frequency distribution in Table 4.

Part 3: Written Introduction and Summary

1. Write an introduction to this application. Discuss the experiment and how it is simulated in this application. Describe the basic components of the application and the statistical concepts that will be applied. The introduction should be at least 50 words and be written with proper grammar and spelling.

2. Write a summary of the application, considering the following topics. The summary should be at least 250 words and be written with proper grammar and spelling. Refer to the tables and graphs (by label and number) throughout the summary. Use the proper statistical terms and symbols in the summary.

- Discuss the binomial probability distribution and other items found in Part 1. This is the theoretical prediction of what should happen.
- Discuss the results of the experiment done in Part 2.
- How do the results of the experiment compare to the prediction of what should happen? Compare the probability that x=2 with the relative frequency for x=2. Compare the expected value with the mean of the relative frequency distribution. Compare the binomial probability distribution with the relative frequency distribution.
- How could the process used with the experiment be changed to get results that are closer to the predicted values?

Format Requirements

- Include a title page with your name, STA2023 Application 3, the word count for the introduction, and the word count for the summary.
- The introduction and summary should be written in paragraphs that are typed and double-spaced, with 1-inch margins and a font size of 12 Times New Roman.
- The introduction should be at least 50 words.
- The summary should be at least 300 words.
- The introduction and summary should be college-level writing with proper grammar and spelling. Do not use first or second person (I, you, etc.).
- Throughout the introduction, tables, calculations, and summary, proper statistical symbols and terms should be used.
- The title page, introduction, tables, calculations, and summary should be a single document (.doc, .docx, or .pdf) which is submitted to the proper Dropbox in Falcon Online by the due date.

Subject | Mathematics |

Due By (Pacific Time) | 10/25/2014 12:00 am |

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