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 2.2 in. A branch of the military requires 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 too tall?

b. If this branch of the military changes the height requirements so that all women are eligible except the shortest 1% and the tallest 2%, what are the new heightrequirements?

Explanation / Answer

a)  percentage of women meeting the height requirement:

as this percentage is very high ; therefore not too many women are denied the opportunity to join this branch of the military the opportunity to join this branch of the military

b)

for bottm 1 percentile ; z score =-2.3263

for whcih corresponding height =mean +z*std deviation =58.28

and for 98th percentile ; z score =2.0537

for whcih corresponding height =mean +z*std deviation =67.92

therefore new height requirement should be 58.28 to 67.92 in

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.