Question

# Male Heights: Assume heights and weights are normally distributed variables with means and standard deviations given...

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

 Strata Mean Standard Deviation Mean Standard Deviation Height Height Weight Weight (inches) (inches) (pounds) (pounds) U.S. Men 69.1 2.9 191 28 U.S. Women 64.0 2.8 145 32 NFL Quarterbacks 76.5 1.8 245 25 Top Female Models 70.0 2.2 115 18

You know a U.S. man who is 78.1 inches tall.

- What is the z-score for his height with respect to other U.S. men? Round your answer to 2 decimal places.

- Would his height be considered unusual for a U.S. man? Why?

- Would his height be considered unusual with respect to NFL quarterbacks? Why?

1) z-score for his height with respect to other U.S. men=(X-mean)/standard deviation =(78.1-69.1)/2.9

=3.10

2)

Would his height be considered unusual for a U.S. man? :Yes ; since absolute value of z score is higher than 2 ; the score should be considered unusual with respect to other U.S. men

3)

z-score for his height with respect to NFL quarterbacks= (78.1-76.5)/1.8 =0.89

since absolute value of z score is less than 2 ; the score should not be considered unusual with respect to NFL quarterbacks