Men\'s heights an normally distributed with mean mu = 69.0 inches and standard d
ID: 3229659 • Letter: M
Question
Men's heights an normally distributed with mean mu = 69.0 inches and standard deviation sigma = 2.8 inches. The U.S marine corps requires that the men have heights between 64 inches and 80 inches. a. Find the percentage of men who meet the height requirements. Are many men denied the opportunity to become a marine because they do not satisfy the height requirements? (proper labeled graph required) b. If the height requirements arc changed so that all men are eligible except the shortest 3% and the tallest 4%, what are the new height requirements? (proper labeled graph required)Explanation / Answer
9) Solution:
a) Find the percentage of men who meet the height requirements.
z(64) = (64-69)/2.8 = -1.7857
z(80) = (80-69)/2.8 = 3.9286
P(64 x 80) = P(-1.79 z 3.93) = 0.9633 = 9.63%
Are many men denied the opportunity to become a Marine because they do not satisfy the height requirement.
Since less than 4% meet the height requirements many men must be denied
entrance.
(b) If the height requirements are changed so that all men are eligible except the shortest 3% and the tallest 4%, what are the new height requirements?
Find the z-value with a 3% left tail: invNorm(0.03) = -1.88
Newer lower requirement would be -1.88*2.8 + 69 = 63.73 inches
Find the z-value with a left tail of 96%: invNorm(0.96) = 1.75
Newer upper requirement would be 1.75*2.8 + 69 = 73.90 inches