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Probability of normal distribution

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data

    find the normal approximation for the binomial probability P(x = 4,5) where n=14 and p = .5.

    2. Relevant equations

    μ = np
    σ = sqrt(npq)

    z = (x - μ)/σ

    3. The attempt at a solution

    p = .5 q = .5

    μ = 14*.5 = 7

    σ = sqrt(14 * .5 * .5) = 1.87

    z = (4 - 7)/1.87 = -1.61

    (my book uses tables to convert the z score into the probability of getting x < 4)

    z = -1.61 = .5 - .4463 = .0537

    The book says the answer is .1812 which is not what i'm getting.


    z =
     
  2. jcsd
  3. Oct 6, 2012 #2
    it's rare that such a simple problem takes this long. let me provide the example from the book

    Screenshot2012-10-06at63129PM.png

    Screenshot2012-10-06at63132PM.png
     
  4. Oct 6, 2012 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    The normal approximation is not very good in this example (because N = 25 is not very large and z is more than 2 standard deviations below the mean). P_exact = 0.0148904, while the continuity-corrected normal approximation is about 0.020152 (so using the normal gives about a 35% error). The normal approximation would be better if N were larger or z were closer to the mean.

    RGV
     
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