statistics

Question

womans height are normally distributed with mean 63.6 in. and a standard deviation 2.5 in. If the U.S Army changes the height requirement so that all women are eligible except the shortests 3% and the tallest 4%, what are the new height requirements?

Answer 1

We need z-scores z_0.96 and z_0.03 to correspond to the tallest and shortest allowed height.

 

Looking up the standard normal table gives z_0.03 = -1.88 and z_0.96 = 1.75

 

So the height requirements to the nearest tenth of an inch are as follows

 

Upper: μ+σz_0.96 = 63.6+2.5(1.75) = 70.0 inches

 

Lower: μ+σz_0.03 = 63.6+2.5(-1.88) = 58.9 inches