Female Heights: Assume heights and weights are normally distributed variables wi

Question

Female Heights: Assume heights and weights are normally distributed variables with means and standard deviations given in the table below.

18

You know a U.S. woman who is 72.8 inches tall.

a) What is the z-score for her height with respect to other U.S. women? Round your answer to 2 decimal places.
z =

(b) Would her height be considered unusual for a U.S. woman?

Yes or No  

(c) Would her height be considered unusual with respect to top female models?

Yes or No    

Strata Mean Standard Deviation Mean Standard Deviation Height Height Weight Weight (inches) (inches) (pounds) (pounds) U.S. Men 69.3 2.8 191 28 U.S. Women 64.1 2.8 145 32 NFL Quarterbacks 76.5 1.8 245 25 Top Female Models 70.0 2.2 115

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Explanation / Answer

Z score = (X - mean)/standard deviation

A) Z = (72.8-64.1)/2.8

= 3.11

B) Z score is greater than 2, so it can be considered unusual

Yes

C) Z = (72.8-70)/2.2 = 1.27

No

(Because the z score is with is (-2,2))

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