Height and length of forearms was measured for 1000 men.
• average height of men was ≈ 1.80 m, SD ≈ 12 cm
• average forearm length ≈ 46 cm, SD ≈ 2.8 cm, r ≈ 0.80
a) What percentage of men have forearms which are 46 ± 2 cm in length?
\bar h = 1.80 +- 0.12
\bar f = 0.46 +- 0.028
r = 0.80
P = 2*\phi(z(0.48)) = 1-2*(1-\phi(0.7142)) = 52%
b) Of the men who are 1.75 m tall, what pergentage have forearms which are 46 ± 2 cm in length?
z(1.75) = -0.42
\cap f = \Phi(r*z(1.75)) = 0.45
SD_{\cap f} = SD_f \sqrt(1-r^2) = 0.0168
P = \phi(z(0.48)) - \phi(z(0.44)) = \phi(1.746) - \phi(0.635) = 70%