Mathematics

Statistics

Western Governors University

### Question Description

**Instructions**

Continuous random variables are interesting to study and appear in all kinds of applications. The height of basketball players on a professional team, ACT scores, bone density test scores, baseball averages, IQ scores, and the length of time you wait for a bus are just a few examples of continuous random variables. This assessment allows you to collect data on any continuous random variable that is interesting to you! You will conduct a survey to collect your data, fit the data you collect to various distribution models, and validate the central limit theorem.

**Survey Procedures**

- Decide what
**continuous, quantitative**data you are going to study. - Describe your sampling method in detail and why you chose that method. You may use cluster, stratified, systematic, or simple random sample using a random number generator, but do not use convenience sampling. If you have another method you would like considered, please contact your instructor for approval.
- Create your survey.
- Conduct a mock survey. Your data size must be at least 150.
- Summarize your data in a meaningful way. Include the following information:
- Define your random variable (X) in words
- Create two lists of your data: unordered data (how it was collected) and in order from smallest to largest

**Data Analysis**

- Find the sample mean and standard deviation (round to 2 decimal places)

- Construct a histogram of your data containing six to ten intervals of equal width. Include labels and scales. Describe the shape of your data.
- Look at three possible distributions of continuous data: Uniform, Exponential and Normal. Which does your data most closely resemble based on the theoretical graphs for these distributions? Discuss and explain your decision. Include a graph of the theoretical distribution you choose.
- Calculate the value
*K*(an X value) that is 1.85 standard deviations above the sample mean. - Using your ordered data set, determine the relative frequencies (round to 4 decimal places) for the following:
- X <
*K* - X >
*K* - X =
*K*

- X <
- Based on the distribution you chose that best fits your data, find the following theoretical probabilities (round to 4 decimal places)
- P(X <
*K*) - P(X >
*K*) - P(X =
*K*)

- P(X <
- Compare your relative frequencies to the corresponding theoretical probabilities. Use this in your discussion of how your data fits the distribution you chose.

**Assignment Checklist**

**Title Page****Written report**on procedures and findings. This includes the explanation of the continuous, quantitative random variable you are studying, a description of the population under study, the sample, and your survey procedures. Include all your answers to the above questions. Be sure to include the information listed under Data Analysis.**Data Collected and Reported.**Two lists of your data: unordered data and in order from smallest to largest. On this page include the sample mean and standard deviation.**Graphs**to include a histogram of your data along with the graph of the theoretical distribution that is the best fit for your data.

**Format**

- doc, docx, xls, xlss
- Style: APA
- Length: 4-6 pages

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