Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By romsek

Thread: Application of Normal Distribution Problem.

  1. #1
    Senior Member
    Joined
    Jul 2015
    From
    United States
    Posts
    366
    Thanks
    6

    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,401
    Thanks
    2290

    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

    $h_l = \Phi^{-1}(0.03) \cdot 2.6 + 63.8 = 58.9~in$
    Thanks from math951
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2015
    From
    United States
    Posts
    366
    Thanks
    6

    Re: Application of Normal Distribution Problem.

    Quote Originally Posted by romsek View Post
    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
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2017
    From
    Lubbock, TX
    Posts
    5

    Question Re: Application of Normal Distribution Problem.

    I have seen this same problem but do not understand what Φ-1 is....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,401
    Thanks
    2290

    Re: Application of Normal Distribution Problem.

    Quote Originally Posted by philenaf View Post
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Mar 15th 2013, 07:13 PM
  2. Application of normal distribution
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Nov 16th 2012, 01:26 PM
  3. A Normal Distribution Problem
    Posted in the Statistics Forum
    Replies: 3
    Last Post: Dec 13th 2010, 02:04 PM
  4. Normal Distribution problem
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 26th 2010, 07:49 PM
  5. application of normal distribution - very lost on how to start
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Jan 30th 2009, 11:36 AM

Search tags for this page


/mathhelpforum @mathhelpforum