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Math Help - Statistics

  1. #1
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    Statistics

    There are four boxes where each box contains nine balls with the number 0 on them and one ball with the number 3 on it. Given that one ball is taken out from each box, determine the mean and standard deviation of the average of the four numbers.

    [Sol] Letting X be the number of balls chosen with the number 3 on them, and Y be the average of the four numbers.

    Y= \frac{3X + 0\cdot (4-X)}{4}

    A few questions.

    Why is Y set up like that? How is it derived?

    Where is 4-X derived?

    Why is Y, set up like that, the average of the 4 numbers?

    In the formula \mu _Y = a \cdot \mu _X + b, what are a and b?
    Last edited by chengbin; October 1st 2009 at 06:34 PM.
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  2. #2
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    Quote Originally Posted by chengbin View Post
    There are four boxes where each box contains nine balls with the number 0 on them and one ball with the number 3 on it. Given that one ball is taken out from each box, determine the mean and standard deviation of the average of the four numbers.

    [Sol] Letting X be the number of balls chosen with the number 3 on them, and Y be the average of the four numbers.

    Y= \frac{3X + 0\cdot (4-X)}{4}

    A few questions.

    Why is Y set up like that? How is it derived?

    Where is 4-X derived?

    Why is Y, set up like that, the average of the 4 numbers?

    In the formula \mu _Y = a \cdot \mu _X + b, what are a and b?
    If X balls have the number 3 on them then 4 - X balls have the number zero on them. The total score is (number of balls with 3 on them)(3) + (number of balls with zero on them)(0) = (X)(3) + (4 - X)(0). Divide by the number of balls (4) to get the average.
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