Height Project-2

Math 123 Quantitative Reasoning Spring 2024 Height Project Put your name, course name, and project name at the top of your Excel spreadsheet and Word document. In this project, you will look at the characteristics of a normal distribution. Part 1: For this project, you need to collect the heights of 9 friends, family, or coworkers, and you will include your own height (for a total of 10 people). You must include at least three women, at least three men, and no children. A table is provided here for you to collect information. First Name Height (in inches) Dinma 66.0 Jacob 73.2 Bernard 64.8 Uzo 74.4 Harry 72.0 Chidinma 68.4 Onyinye 66.0 Chioma 69.6 Ngozi 66.0 Rose 70.8 Part 2: The heights of adult men in the United States are approximately normally distributed with a mean of 70 inches and a standard deviation of 3 inches. Heights of adult women are approximately normally distributed with a mean of 64.5 inches and a standard deviation of 2.5 inches. In Excel, create two tables, one for men and one for women. Label each table to identify which is men and which is women. Each table should have columns for first name, height (in inches), z-score, and probability. Add borders to your tables to clearly show each separate table. You must use Excel to find the z-score. Excel does not have a function to find the z-score, but you can enter a formula into Excel and drag it down the column to apply to all people in that table. Round z-score to the nearest hundredth. Excel has a function that will find the probability, so you do not need the z-score table. The Excel function is =NORM.S.DIST( z ,TRUE) You will enter the z-score for z in the formula, and all other parts of the formula are identical to what is provided here. Round probability to the nearest hundredth. Answers these questions in your Word document:

Math 123 Quantitative Reasoning Spring 2024 1. Look at all ten people and locate the person with the lowest z-score. Do you think this person’s height is unusual? Explain your answer quantitatively. The person with the lowest z-score is Bernard with a z-score of -1.73 and a height of 64.8 inches. Bernard's height is unusual as there is a 9 percent chance that a randomly selected U.S. person would be the same height as Bernard. This also means that his height is lower than the mean. 2. Look at all ten people and locate the person with the highest z-score. Do you think this person’s height is unusual? Explain your answer quantitatively. The person with the highest z-score is Rose with a z-score of 2.52 and a height of 70.8 inches. Rose's height is not unusual as there is a 99 percent chance that a randomly selected U.S. person would be the same height as her. This also means that her height is bigger than the mean.

Math 123 Quantitative Reasoning Spring 2024 Notes:  This question will require guess-and-check in Excel. You can complete this question on the same spreadsheet as your tables from Part 2. Label your work in Excel. For example, label it “Part 4” then put your work under or to the side.  You will notice on the rubric that no points are awarded for the correct height. Points are awarded for your explanation of the process. The last step of explaining your process should be stating the height.  Start by stating your initial test value and why you chose that value, based on what you know about normal distributions, z-scores, the Empirical Rule (68-95-99.7 Rule), and maybe even the people in your table from Part 2. Then, explain your process to find the correct value.  Lastly, state the height in feet with inches as a remainder (for example, 5 feet 9.25 inches).

Math 123 Quantitative Reasoning Spring 2024 Rubric for Height Project: Points 0 1 2 3 4 Part 1 – Data Collection - Heights for 10 people - Heights listed in inches - At least 3 women - At least 3 men Spreadsheet did not include any of the required items. Spreadsheet missing three of the items. Spreadsheet missing two of the items. Spreadsheet missing one of the items. Spreadsheet includes all items. Part 2 - Two tables - Tables are labeled men, women - Four columns in tables - Added borders Spreadsheet has none of the required items. Spreadsheet missing three of the items. Spreadsheet missing two of the items. Spreadsheet missing one of the items. Spreadsheet includes all items. Part 2 Calculations - Used correct info for men, and for women - Found z-score using Excel - Found probability using Excel formula - Rounded correctly Spreadsheet has none of the required items. Spreadsheet missing three of the items. Spreadsheet missing two of the items. Spreadsheet missing one of the items. Spreadsheet includes all items. Part 2 Questions - Lowest unusual? - Explain quantitatively? - Highest unusual? - Explain quantitatively? Document did not include any of the required items. Document missing three of the items. Document missing two of the items. Document missing one of the items. Document includes all items. Part 3 - 18-inch height range - Explain men quantitatively - Explain women quantitatively - Range encompasses majority of Americans Document has none of the required items. Document missing three of the items. Document missing two of the items. Document missing one of the items. Document includes all items. Part 4 - How chose initial test value? - Process of increasing or decreasing test value - How you knew you had correct value - How value was applied to find person’s height Document has none of the required items. Document missing three of the items. Document missing two of the items. Document missing one of the items. Document includes all items.