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Math Help - Normal Distribution Problem -

  1. #1
    Yan
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    Normal Distribution Problem -

    Suppose X is a random variable with mean 3 and variance 4.
    X1....X100 are independent random variables, each of which has the
    same distribution as X. Let Y be the average of these variables (the sum divided by
    100). Find a good approximation of P [|X-3|>0.5]?


    my answer is 0.0124. Is that right?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Yan View Post
    Suppose X is a random variable with mean 3 and variance 4.
    X1....X100 are independent random variables, each of which has the
    same distribution as X. Let Y be the average of these variables (the sum divided by
    100). Find a good approximation of P [|X-3|>0.5]?


    my answer is 0.0124. Is that right?
    Yes

    CB
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  3. #3
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Yan View Post
    Suppose X is a random variable with mean 3 and variance 4.
    X1....X100 are independent random variables, each of which has the
    same distribution as X. Let Y be the average of these variables (the sum divided by
    100). Find a good approximation of P [|X-3|>0.5]?



    my answer is 0.0124. Is that right?
    You mean P [|Y-3|>0.5]=1-P(2.5<Y<3.5)

    where Y is approximately normal with mean 3 and st dev 1/5.
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