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Math Help - random variable?/probability question

  1. #1
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    random variable?/probability question


    I normally can figure out these straightforward statistics problems, but this one has got me stumped! Thanks in advance to anybody who offers insight.

    A summer resort rents rowboats to customers but does not allow more than four people to a boat. Each boat is designed to hold no more than 800 pounds. Suppose the distribution of adult males who rent boats, including their clothes and gear, is normal with a mean of 190 pounds and standard deviation 10 pounds. If the weights of individuals passengers are independent, what is the probability that a group of four adult males passengers will exceed the acceptable weight limit of 800 pounds?

    (A) 0.023
    (B) 0.046
    (C) 0.159
    (D) 0.317
    (E) 0.977
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  2. #2
    MHF Contributor
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    You should have your concept of linear functions of random variables.

    For a random variable X

    \mu_{X} = 190 = E[X]

    \sigma_{X} = 10

    \sigma_{X}^{2} = 100 = Var(X)

    For four random variables X_{i}, which are iid as X, i \epsilon \{1, 2, 3, 4\}

    And Y = X_{1}+X_{2}+X_{3}+X_{4}

    E[Y] = 4*E[X] = 4*190 = 760

    Var(Y) = 4*Var(X) = 4*100 = 400

    \sigma_{Y} = \sqrt{400} = 20

    Now what?
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