A survey found that women\'s heights are normally distributed with mean 63.4 in

Question

A survey found that women's heights are normally distributed with mean 63.4 in and standard deviation 2.4. A branch of the military rewires women's heights to be between 58 in and 80 in. A. Find the percentage of women meeting the height requirement Are many women being denied the opportunity to join this branch of the military because they are too short or tail? b. If this branch of the military changes the height requirements so that all women are eligible except the shorted 1% and the tallest 2% what are the new height requirements? a. The percentage of women who meet the height requirements is

Explanation / Answer

a) P(58<X<80)= P((58-63.4)/2.4<Z<(80-63.4)/2.4)=P(-2.25<Z<6.9167)=1-0.0122=0.9878~98.78%

b)for shortest 1%, z=-2.3264 ; hence corresponding score =63.4-2.3264*2.4=57.82 in

for tallest 2%, z=2.0538 ; hence corresponding score =63.4+2.0538*2.4=68.33 in

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