Mathematics Homework Help

PART 1:Airshow Day 2: Probability

Introduction

This discussion introduces you to normal probability via the calculated z-score. A z-score converts a non-standard normal distribution into a standard normal distribution; a standard normal distribution has a mean of zero and standard deviation of one.

Additional z-score properties and details are provided later in the course. For this assignment, what is needed is the capability to calculate a z-score and find its associated probability (see Table A-2 in your textbook). Here is an example:

• Excel equation: z = (Your Score (X) – Mean)/(Standard Deviation) OR z = (X – Mean)/S.
• Z-score and probability calculation example:
  • Assume Intelligent Quotient (IQ) scores are normally distributed with a Mean of 100 and Standard Deviation of 15.
  • Assume a friend has an IQ score of 130 (X).
  • The z-score is then calculated: z = (130 – 100)/15 = 30/15 = 2.00.
  • Find Table A-2 in your textbook. The probability (green shaded area) associated with z = 2.00 is p = 0.9772.
  • The probability of another friend scoring “higher” (non-shaded area) than 130 is: p = (1.0000 – 0.9772) = 0.0228 or 2.28%.
  • As always, SKETCH the problem. It will help you to answer all questions.

Scenario

Day 2 of the airshow arrives, and the weather is worsening. The temperature is 50oF, and strong thunderstorms are predicted. Continuing intermittent moderate to strong runway crosswinds (25 Knots sustained, with gusts to 40 Knots). Fortunately, all Day 2 flying sorties are accomplished with only minor incidents.

Your team collected these simulated data for Day 2 flying sorties:

Module 3 Airshow Discussion Excel Template-2.xlsx

Complete

In Microsoft Excel, complete the “Airshow – US Military Aircraft Performance” table by calculating the column and row values for mean, population standard deviation, and z-score column values (use Sortie 10’s mean as the value of “X” in the z-score equation); report your calculated values to two decimal places (i.e., 0.12). For reporting probability, i.e., (greater than your z-score), use Table A-2 in your textbook and report the value of p to four decimal places (i.e., 0.1234).

Save your work as a file to your computer and then read the Canvas instructions on How do I embed an image in a discussion reply as a student? (Links to an external site.)

Post & Discuss

Embed the image (you must embed!) of your spreadsheet into the discussion area along with a narrative (interpretation and understanding) of your findings before the fourth day of the module week to receive full credit. Return at least twice later in the module week to provide meaningful (substantive) comments to two or more of your classmates’ posts. DO NOT “post and run” – making all three posts in the same visit. You need multiple visits to the discussion area to gain multiple perspectives by reading all of the posts and replies.

Review the Discussion Rubric for detailed grading information.

PART2:Airshow Day 2: Airshow Champion

Scenario

During Day 2 of the airshow, you are required to select and report an Airshow Champion. Use the spreadsheet that you created for the Module 3 – Discussion: Airshow Day 2: Probability discussion to:

1. Determine the aircraft winner.
2. Report the probability of another aircraft scoring higher than the winner.

Report values of probability to four decimal places, i.e., p = 0.1234.

Report the Champion

Now that you have the simulated data, report the Airshow Champion. Report the champion in a Memorandum of Understanding (MOU). Your MOU should be a maximum of one page with one-inch margins using 11 point font and consist of only the following three paragraphs:

1. Introduction – Prepare the audience for what he/she is about to read.
2. Results – The facts.
3. Conclusion(s) – Results based, concise and to the point; actionable.

Review the Writing Suggestions page for tips. Use this format for your document:

MEMORANDUM OF UNDERSTANDING

TO: 97th AMW – USAF

FROM: Your Name

DATE: Add Assignment Due Date

SUBJECT: Determined by Student

Submit

Save your assignment using a naming convention that includes your first and last name and the activity number or description (i.e., STAT 211_Last_Name_First_Name_Module_3). Do not add punctuation or special characters.

This assignment will automatically be checked through Turnitin, a service that checks your work for improper citation or potential plagiarism by comparing it against a database of web pages, student papers, and articles from academic books and publications.

Review the Assignment Rubric for detailed grading information.