Question

According to the National Center for Health Statistics, the mean height of an American male is 69.3 inches and the mean height of an American female is 63.8 inches. The standard deviation for both genders is 2.7 inches.

Assuming that heights among a single gender are normally distributed. Find the z-score for your height in inches using the mean of your own gender and then find the percentile at which you fall among people of your own gender using the percentile table.

A Microsoft Excel spreadsheet is required

Answer 1

Solution:-

For male mean=69.3 and standard deviation =2.7

For Female mean=63.8 and standard deviation =2.7

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Male

Supoose you are male with height 70 inch then x=70

Z-score for your height is z=(x-69.3)/2.7 =(70-69.3)/2.7=0.2592

percentile=NORM.DIST(z,0,1,1)=NORM.DIST(0.2592,0,1,1)=0.60.22=60th percentile

Z-score =0.2592

percentile=60th percentile

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Female

Supoose you are female with height 65 inch then y=65

Z-score for your height is z=(y-63.8)/2.7 =(65-63.8)/2.7=0.4444

percentile=NORM.DIST(z,0,1,1)=NORM.DIST(0.4444,0,1,1)=0.6716=67th percentile

Z-score =0.4444

percentile=67th percentile

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