Week 4 Discussion: The US Population Statistics, Z-Scores (Coursework Sample)
Week 4
This week's focus is the Normal distribution, a very important concept in statistics. For this discussion you will compare several attributes about yourself to the U.S. population using a Normal Distribution. The attributes are:
1) Height (Average US male :69.7 inches, 2.8 inch standard deviation; Average US Female: 64.4 inches, 2.4 inch standard deviation)2) Shoe Size (Average US male :10.5, 1.5 standard deviation; Average US Female: 8.75 (men's size), 1.25 standard deviation)3) Ring Size (Average US male: Size 9, 1 standard deviation; Average US female: 6, 1 standard deviation)Measure your height to the nearest half-inch unless you know it. Determine your most commonly used shoe size (using men's sizes). To find ring size, measure the circumference of your ring finger with a slim piece of paper and a ruler or a tape measure ribbon and use the following chart (or if you already know it, use that number):
Size 4: 1 13/16 inches
Size 5: 1 15/16 inches
Size 6: 2 1/16 inches
Size 7: 2 1/8 inches
Size 8: 2 1/4 inches
Size 9: 2 5/16 inches
Size 10: 2 7/16 inches
Size 11: 2 9/16 inches
Size 12: 2 5/8 inches
Size 13: 2 3/4 inches
Size 14: 2 7/8 inchesThen calculate the z-score associated with your three measurements using the above US averages for your gender. Are you above or below average? Then, assuming Normality, use the z-table, an online calculator, or Excel to determine the percentage of people who are smaller than your measurements in all three areas. Add any insights, comments, or personal experience to elaborate on your post. For example, if you are determined to be shorter/taller than average, is this surprising to you based on your experience? Your replies to other students may be comparing your measurements or anything else of relevance. My measurements are:
5’3” Height
Size 9 Ring size
Women Shoe size: 9 ½ in men my size is 8
Week 4 Discussion – Statistics
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Institution
Week 4 Discussion - Statistics
My comparative measurements are as follows;
Height: 5'3†or 63 inches
Women shoe size: 91/2 or 8 in men
Ring size: 8
To compare the relative individual measurements to the US population statistics, we will need to calculate the z-scores for each of the three individual measurements using the formula below.
Z-score = (x - µ)/σ where x is the individual measurement given above for each case, µ is the population mean and σ is the population standard deviation. In order to infer on the relative proportion of the measurements from the z-score values obtained, we shall assume that the US population statistics is obtained from normally distributed population parameters CITATION Hel15 \l 1033 (Helio, Dani, & Francisco, 2015).
Height
Z-score = ( 63 – 64.4)/2.4 = -0.58
Using the z-table, the proportion of US citizen who are shorter than me is 0.2810. Therefore 28.1% of the US female population are shorter than me. This justifies the common reference by my friends and family as a short lady.
Shoe size
z-score = (8 – 8.75)/1.25 = -0.6
Using the z-table, the proportion of US citizen with a smaller shoe size than mine...
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