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Conditional normal probability, repost

  1. May 8, 2013 #1
    1. The problem statement, all variables and given/known data

    The number of hours of sunshine in one week in a specific resort is assumed to follow a normal distribution with expectation 43 and standard deviation 17.

    Family A will spend the first three weeks of the summer at the resort. Family B will spend the LAST two weeks of the summer at the resort.

    Assuming everything is independent, what is the probability that family A will get atleast twice as much sunshine as family B?

    2. Relevant equations

    A = # of sunshine hours for family A
    B = # of sunshine hours for family B

    3. The attempt at a solution

    E(A) = 3*E(X) = 129
    σ(A) = sqrt(3)*σ(X) = 29.4

    E(B) = 86
    σ(B) = sqrt(2)*σ(X) = 24

    So A ~ N(129, 29.4), B ~ N(86, 24)

    If we let Z = A/B and try to find P(Z > 2), we do not have a linear combination of normally distributed random variables so I guess that's not the right way to go, assuming we want to do the normal table reading thing. So I don't know where to go from here. Help!
  2. jcsd
  3. May 8, 2013 #2


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    Staff: Mentor

    You could try an integration over A or B, and see if that works.

    Edit: Oh, I did not see this. Follow awkward's hint, that is way easier.
    Last edited: May 8, 2013
  4. May 8, 2013 #3
    Hint: What can you say about the distribution of the random variable A - 2B?
  5. May 9, 2013 #4
    D'oh! Thank you so much!
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