Question

The upper arm length of females over 20 years old in the United States is approximately Normal with mean 35.8 cm and standard deviation 2.1 cm. According to the 68-95-99.7 Rule, what percent of women over 20 have upper arm length between 33.7 cm and 35.8 cm?

Answer 1

mean ()  = 35.8

standard deviation () = 2.1

percent of women over 20 have upper arm length between 33.7 cm and 35.8 cm is

one standard deviation bellow the mean.

= -

=35.8 - 2.1

= 33.7

According to the 68-95-99.7 Rule,

one standard deviation above and bellow the mean Contains 68 %

But we want to find percentage for bellow the mean.

Hence,

one standard deviation bellow the mean = 68/2 =34%

34 %  percent of women over 20 have upper arm length between 33.7 cm and 35.8 cm