69.5 in. and standard deviation 2.4 in Men\'s heights are normally distributed w

Question

69.5 in. and standard deviation 2.4 in Men's heights are normally distributed with mean . normally distributed with mean 63.8 in. and standard deviation 2.6 in. Problem 1: Navy Pilots. The US Navy requires that fighter pilots have heights between 62in. and 78in. 1. Find the percentage of women meeting the height requirement. Are many women not qualified because they are too short or too tall? 6 3.8t Find the percentage of men meeting the heights requirement. Are many men not qualified because they are too short or too tall? 2. 3. If the Navy chances the height requirements so that all women are eligible except the shortest 1% and the tallest 1%, what are the new height requirements for women? 4. If the Navy ch ances the height requirements so that all men are eligible except the shortest 1% and the tallest 1%, what are the new height requirements for m en?

Explanation / Answer

Ans:

1)

z(62)=(62-63.8)/2.6=-0.692

z(78)=(78-63.8)/2.6=5.462

P(-0.692<z<5.462)=1-0.2444=0.7556

75.56% of women meet requirement. and 24.44% are too short or tall.

2)

z(62)=(62-69.5)/2.4=-3.125

z(78)=(78-69.5)/2.4=3.542

P(-3.125<z<3.542)=0.9998-0.0009=0.9989

99.89% of men meet the requirement and very few 0.11% are too short or tall.

3) z value for 1% cut off will be +/-2.33

lower limit=63.8-2.33*2.6=57.74

upper limit=63.8+2.33*2.6=69.86

4)

lower limit=69.5-2.33*2.4=63.91

upper limit=69.5+2.33*2.4=75.09

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