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Normal Distribution Question

  1. Jul 3, 2017 #1
    1. The problem statement, all variables and given/known data
    Suppose that X ~ N(μ,σ). Find a in terms of μ and σ if P(X>a) = 1/3 * P(X ≤a)

    2. Relevant equations


    3. The attempt at a solution
    1 - P(X ≤a) = 1/3 * P(X ≤a)
    3 = 4P(X ≤a)
    P(X ≤a) = 3/4

    Since x0 = μ + σz0 where x0 and z0 are the same percentile for N(μ,σ) and N(0,1) (respectively), then z0 = 0.67449 (by invNorm(0.75, 0, 1)). It follows that

    a = μ + 0.67449σ

    I'm not sure if this is the correct method, someone in my class solved it another way and got a different answer, but this seems to make sense to me.

    Regards,

    Michael
     
  2. jcsd
  3. Jul 3, 2017 #2

    Charles Link

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    Homework Helper

    I agree with your solution. Also please read my last comments on your Poisson distribution problem of last week. I think you'll find them of interest. That was actually the first time I had looked at the Poisson distribution in this much detail, and the two methods of solving the same problem are both quite interesting.
     
  4. Jul 3, 2017 #3

    Ray Vickson

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    It is the correct method, and the answer is correct.
     
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