**Case Assignment**

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results. Submit your work in a typed Microsoft Word document.

- The final exam scores listed below are from
section of MATH 200. How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?*one*

99 34 86 57 73 85 91 93 46 96 88 79 68 85 89

- The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?
- If you know the standard deviation, how do you find the variance?
- To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. The prices he was quoted are listed below:

$216 $135 $281 $189 $218 $193 $299 $235

Find the standard deviation.

- A company has 70 employees whose salaries are summarized in the frequency distribution below.

Salary |
Number of Employees |

5,001–10,000 | 8 |

10,001–15,000 | 12 |

15,001–20,000 | 20 |

20,001–25,000 | 17 |

25,001–30,000 | 13 |

- Find the standard deviation.
- Find the variance.
- Calculate the
**mean**and**variance**of the*sample*data set provided below. Show and explain your steps. Round to the nearest tenth.

14, 16, 7, 9, 11, 13, 8, 10

- Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)

3, 5, 1, 6, 1, 2, 2, 6, 3, 4, 5, 1, 1, 3, 4, 2, 1, 6, 5, 3, 4, 2, 1, 3, 2, 4, 6, 5, 3, 1

- Answer the following questions using the frequency distribution table you created in No. 7.
- Which number(s) had the highest frequency?
- How many times did a number of 4 or greater get thrown?
- How many times was an odd number thrown?
- How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?
- The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the data below, find the following for each sample.
- Range
- Standard deviation
- Variance

Lastly, compare the two sets of results.

Company |
Wait times in seconds |
|||||||

Big Burger Company | 105 | 67 | 78 | 120 | 175 | 115 | 120 | 59 |

The Cheesy Burger | 133 | 124 | 200 | 79 | 101 | 147 | 118 | 125 |

- What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

*.*

**Module 3 – SLP**

**Frequency Distributions**

Continuing with the data you collected in the Module 1 SLP, (attached below) write a paper (1- to 3-page, typed Word document) including all of the following content:

- Include your data from Module 1.
- Create a frequency distribution table for your data. You can use Excel or Word.
- Calculate the standard deviation.
- Calculate the variance.
- Is this a normal distribution? How do you know?
- What are the implications?

*Submit your paper at the end of Module 3.*

**SLP Assignment Expectations**

Answer all questions posted in the instructions. Use information from the modular background readings and videos as well as any good-quality resource you can find. Cite all sources in APA style and include a reference list at the end of your paper.

Note about page length: Your ability to clearly articulate and explain these concepts is being assessed. The page length is a general guideline. A 3- or 4-page paper does not necessarily guarantee a grade of “A.” An “A” paper would include detailed information and explanations of all the assignment requirements listed above. The letter grade will be based upon demonstrated mastery of the content and ability to articulate and apply the concepts in the assignment. Keep this in mind while writing your paper.

*Your paper should follow the academic writing format and APA format given in “Writing Style Guide” and “Writing Workshop” on TUI web portal “My resources” tab.*