Question

Use the data found in this chart to answer the following questions.

Strata	Mean Height (inches)	Standard Deviation Height (inches)	Mean Weight (pounds)	Standard Deviation Weight (pounds)
U.S. Men	69.3	2.8	191	28
U.S. Women	64	2.8	145	32
NFL Quarterbacks	76.5	1.8	245	25
Top Female Models	70	2.2	115	18

For the given heights of U.S. men, calculate the zz-score, and comment on whether the height would be unusual for a U.S. man.

(a) 74.7
zz-score:
Unusual
Not unusual

(b) 70.6
zz-score:
Unusual
Not unusual

(c) 76.5
zz-score:
Unusual
Not unusual

(d) 62.2
zz-score:
Unusual
Not unusual

Answer 1

a)

z score=(X-mean)/standard deviation=(74.7-69.3)/2.8=1.93

since absolute value of z score is less than 2 ; this is not unusual

b)

z score=(X-mean)/standard deviation=(70.6-69.3)/2.8=0.46

since absolute value of z score is less than 2 ; this is not unusual

c)

z score=(X-mean)/standard deviation=(76.5-69.3)/2.8=2.57

since absolute value of z score is greater than 2 ; this is unusual

d)

z score=(X-mean)/standard deviation=(62.2-69.3)/2.8= -2.54

since absolute value of z score is greater than 2 ; this is unusual