Question

Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.

Height (inches)		Gender
61		M
64		F
65		F
65		F
65		F
67		F
67		F
67		F
68		M
68		F
68		M
69		F
69		M
69		F
69		F
69		M
70		M
70		F
70		F
70		F
71		M
71		M
71		M
72		F
72		F
72		M
72		M
72		F
72		M
72		M
72		F
73		M
73		M
74		M
75		M

Answer 1

data is 61,64,65,65,65,67,67,67,68,68,68,69,69,69,69,69,70,70,70,70,71,71,71,72,72,72,72,72,72,72,72,73,73,74,75

mean = μ =sum (61,64,65,65,65,67,67,67,68,68,68,69,69,69,69,69,70,70,70,70,71,71,71,72,72,72,72,72,72,72,72,73,73,74,75) /35

=2434/35

=69.5428

sd =σ =√ (∑(x-μ)^2 /(n-1))

= 3.08071

Using emperical rule,68 % data lies between z=-1 and z=1

so for z=-1

x1 =z*σ +μ

=-1*3.08071 +69.5428

=-3.08071+69.16142

=66.46

For z=1

x2 =z*σ +μ

=1*3.08071 +69.5428

=3.08071+69.16142

=72.24

So,68% of female height are between 66.46 and 72.24

answered by: anonymous