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[Statistic] NCE or just usual z-score?

  1. Oct 6, 2008 #1
    1. The problem statement, all variables and given/known data
    In an ancient culture, the average male life span was 37.6 years, with a standard deviation of 4.8 years The average female life span was 41.2 years, with a standard deviation of 7.7 years. use the properties of the normal distribution to find the following:
    a. What percentage of men died before age 30?
    b. What percentage of women lived to an age of at least 50?
    c. At what age is a female death at the same relative position in the distribution as a male death at age 35?

    2. Relevant equations
    [tex]X'=s'z+\overline{X}[/tex]
    using Standard Normal Distribution table to find percentile rank

    3. The attempt at a solution
    Problem a a is clear for me, but I have a little doubt in b, because
    I am confused about choosing between [tex]PR_{49.9}[/tex] or [tex]PR_{50}[/tex]? Percentile rank is defined as at or below. So, if it is said at least, I have to choose lower number, but what is it? Is it 49.9; 49.99; 49.999; or... So that's why I think [tex]PR_{50}[/tex] is the best [​IMG]

    Problem c is just using z-score right? So I don't have to apply Normal Curve Equivalent here? Finding z-score for male rate, then using mean and standard deviaton for female rate, then that's the answer. Is it right?

    Thanks for the answer. [​IMG] [​IMG] [​IMG]
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 6, 2008 #2

    statdad

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    Homework Helper

    If you want the percentage of women who lived to at least [tex] 50 [/tex] you want to calculate

    [tex]
    \Pr(X \ge 50)
    [/tex]

    For the second question (I think this is what you are saying) if you can determine how many standard deviations [tex] 35 [tex] is from the mean lifetime for men, you need to find the age for women that is the same number of standard deviations from their mean.
     
  4. Oct 6, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since the normal distribution is a continuous distribution, not just integer valued, the probability a woman will live to be "exactly" 50 is 0 (the integral of the probility density "from 50 to 50" is 0). The probability a woman will live to be "greater than or equal to 50" and "greater than 50" are the same.
     
  5. Oct 8, 2008 #4
    So, it is 100%-PR(50), right?
    Gosh, I do it with PR (49.9) [​IMG]
     
  6. Oct 8, 2008 #5
    --EDITED--
    Double post, sorry. [​IMG]
     
    Last edited: Oct 8, 2008
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