# Thread: Application of Normal Distribution Problem.

1. ## Application of Normal Distribution Problem.

Us airforce requires pilots to have heights between 64 in. and 77 in.

Men: mean: 69.5 inches. standard deviation 2.4 inches.

Women: mean: 63.8 inches. Standard deviation 2.6 inches.

I found that 47.2 percent of women meet the height requirement. While 98.81 percent of men meet the height requirement.

How do I answer the last part: If the Air Force height requirements are changed to exclude only the tallest 3 percent of men and the shortest percent of women, what are the new height requirements?

So I know doing this, will change the mean, and standard deviation, but I cannot grasp how to calculate this ;o. I am thinking, would i just deduct 3 percent from both original requirements, then I get 95.51 percent for men meeting the requirement, and 44.2 for women.

Then once I got that, I can find the according area that matches with the results, to get the z score of each data, then after that, I can calculate the mean.? What do you guys think.

2. ## Re: Application of Normal Distribution Problem.

I think you should just solve the thing w/o shortcuts.

Excluding only the tallest 3% of men results in an upper limit of

$h_u = \Phi^{-1}(0.97) \cdot 2.4 + 69.5 = 74.0~in$

Excluding only the shortest 3% of women results in a lower limit of

$h_l = \Phi^{-1}(0.03) \cdot 2.6 + 63.8 = 58.9~in$

3. ## Re: Application of Normal Distribution Problem.

Originally Posted by romsek
I think you should just solve the thing w/o shortcuts.

Excluding only the tallest 3% of men results in an upper limit of

$h_u = \Phi^{-1}(0.97) \cdot 2.4 + 69.5 = 74.0~in$

Excluding only the shortest 3% of women results in a lower limit of

$h_l = \Phi^{-1}(0.03) \cdot 2.6 + 63.8 = 58.9~in$
oh jeesh Thanks Romsek, I got it! ;D

4. ## Re: Application of Normal Distribution Problem.

I have seen this same problem but do not understand what Φ-1 is....

5. ## Re: Application of Normal Distribution Problem.

Originally Posted by philenaf
I have seen this same problem but do not understand what Φ-1 is....
$\Phi^{-1}(x)$ is the inverse of the CDF of the standard Normal distribution.