Question

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?

Answer 1

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