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Math Help - probabilities- Please more detail that will easy for me to understand

  1. #1
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    probabilities- Please more detail that will easy for me to understand

    • Assume random variable x is from a normal distribution with mean = 20 and standard deviation σ = 5, find the following probabilities:

    a. P(14.735 x 30.325)
    b. P(9.225 x 35)
    c. P(x 27.5)
    d. P(25 x 29.175)

    • Given the profit payoff table below:
    Decision alternative-d1 State of Nature s1



    s1 s2 s3 s4


    d1 12 9 10 4
    d2 14 10 8 6
    d3 9 12 15 11
    d4 8 10 11 13











    Suppose the manager has no probability information, what is the decision recommendation for him using the optimistic, conservative, and min-max regret approach?
    Last edited by lillian; August 2nd 2007 at 08:30 AM. Reason: miss the table
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  2. #2
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    in the part of calculating the probabilities, use the fact that:

    P(a<x<b)=F(b)-F(a)

    in your case, it's normal distribution, so what you have to do is to standarize every value:

    z=(x-mu)/sigma
    ( z=(x-mean)/s.d)

    and then just check the table of the standarized normal distribution
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  3. #3
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    My answer- thanks for help :)


      • P(14.735 x 30.325)
    For value of 14.735
    Z = (14.735 20)/5= -1.053
    Probability from table = 0.3531

    For value of 30.325
    Z = (30.325 20)/5= 2.065
    Probability from table = 0.4808
    P(14.735 x 30.325) = 0.4808 + 0.3531 = 0.8339
      • P(9.225 x 35)
    For value of 9.225
    Z = (9.225 20)/5= -2.155
    Probability from table = 0.4846

    For value of 35
    Z = (35 20)/5= 3
    Probability from table=0.4986
    P(9.225 x 35) = 0.4846 + 0.4986 = 0.9832
      • P(x 27.5)
    For value of 27.5
    Z = (27.5 20)/5 = 1.5
    Probability from table = 0.4332
    From table, for z=1.5, value is 0.4332
    Probability P(x 27.5) = 0.5+ 0.4332 = 0.9332
      • P(25 x 29.175)
    For value of 25
    Z = (25 20)/5= 1
    Probability from table = 0.3413

    For value of 29.175
    Z = (29.175 20)/5= 1.835
    Probability from table = 0.4671
    P(25 x 29.175) = 0.4671- 0.3413= 0.1258
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