Question 564035
Men's heights are normally distributed with 
mean 59.0 and standard deviation 2.8in.
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Question: Marine Corps height requirement for men. The US Marine Corps requires that men have heights between 64 in. and 80 in.
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(a) Find the percentage of men who meet the height requirements. 
z(64) = (64-59)/2.8 = 1.7857
z(80) = (80-59)/2.8 = 7.5
P(64 <= x <= 80) = P(1.78457<= z <=7.5) = 0.0371 = 3.71%
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Are many men denied the opportunity to become a Marine because they do not satisfy the height requirement.
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Since less than 4% meet the height requirements many men must be denied
entrance.
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(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 + 59 = 53.73 inches
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Find the z-value with a left tail of 96%: invNorm(0.96) = 1.75
Newer upper requirement would be 1.75*2.8 + 59 = 63.90 inches

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Cheers,
Stan H.