. Assume women\'s heights are normally distributed with mean 63.8 in. and standa

Question

. Assume women's heights are normally distributed with mean 63.8 in. and standard deviation 2.6 in. The U.S. Air Force requires pilots have heights between 64 in. and 77 in. a) Find the percentage of women meeting the height requirement. are many women not qualified because they are too short or too tall? Enter your answer as a percentage. ) If the Air Force height requirements are changed so that all women are eligible except the shortest of 2% and the tallest 2%of women, what are the new height requirements?

Explanation / Answer

Here mean=63.8 and sd=2.6

a. We need to find P(64<x<77)

Converting to z we get P(0.08<z<5.08)=0.4681=46.81%

Here we need to find P(z<64 or z>77)=P(z<0.08 or z>5.08)=0.5319=53.19%

b. Here we need find x1 and x2 when

P(x<x1 or x>x1)=0.02

Using z table we get z1=-2.327

Hence x1=-2.327*2.6+63.8=57.75

And x2=2.327*2.6+63.8=69.85

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