Question

Using the empirical rule, 95% of female 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,95 % data lies between z=-2 and z=2

so for z=-2

x1 =z*σ +μ

=-2*3.08071 +69.5428

=-6.16142+69.16142

=63.38

For z=2

x2 =z*σ +μ

=2*3.08071 +69.5428

=6.16142+69.16142

=75.70

So,95% of female height are between 63.38 and 75.70

answered by: anonymous