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Math Help - Normal Distribution Problem.

  1. #1
    Newbie Firstone's Avatar
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    Normal Distribution Problem.

    The weights of mandarins in a large crate have a Normal distribution with μ = 110 grams and σ = 16.7 grams. Consider the random process of picking three mandarins independently and putting them in a bag. The standard deviation of the total weight of the three mandarins in the bag is?

    Any help would be greatful. =)
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  2. #2
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    Quote Originally Posted by Firstone View Post
    The weights of mandarins in a large crate have a Normal distribution with μ = 110 grams and σ = 16.7 grams. Consider the random process of picking three mandarins independently and putting them in a bag. The standard deviation of the total weight of the three mandarins in the bag is?

    Any help would be greatful. =)
    Let X be the random variable weight of a single mandarin.
    Let Y be the random variable weight of a three mandarins.

    Then Y = 3X.

    You should know that \sigma^2_Y = 3^2 \sigma^2_X \Rightarrow \sigma_Y = 3 \sigma_X = \, ....

    In general, if Y = aX + b then \mu_Y = a \mu_X + b, \sigma^2_Y = a^2 \sigma_X^2 and \sigma_Y = |a| \sigma_X.
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  3. #3
    Newbie Firstone's Avatar
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    I'm abit lost in how to do that.

    Could someone give me a numeric answer please.
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  4. #4
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    Quote Originally Posted by Firstone View Post
    I'm abit lost in how to do that.

    Could someone give me a numeric answer please.
    So you've 'progressed' from "Any help would be greatful (sic)" to wanting the whole thing done for you. Sheesh ......

    \sigma_Y = 3 \sigma_x and \sigma_X = 16.7.

    Surely you can substitute numbers into a simple formula ....!?
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