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Math Help - normal distribution question

  1. #1
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    normal distribution question

    ok not sure what im doin wrong with question hope someone can help.

    The randow variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P(X<x) = 0.025

    this is how i attempt to solve it -

    X~N(16,0.8)

    (X-16)/0.8=0.025

    X=16.02

    but i be doin it wrong me think :/

    any suggestions??

    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by djmccabie View Post
    ok not sure what im doin wrong with question hope someone can help.

    The randow variable X has a normal distribution with mean 16 and variance 0.64. Find x, such that P(X<x) = 0.025

    this is how i attempt to solve it -

    X~N(16,0.8)

    (X-16)/0.8=0.025

    X=16.02

    but i be doin it wrong me think :/

    any suggestions??

    thanks

    X\sim N(16,0.8^2)

    so: Z=(X-16)/0.8 \sim N(0,1)

    The value of z such that:

    Pr(Z<z)=0.025

    is obtained by reverse look up in a table of the standard normal distribution, and that tells us that:

    Pr(Z<1.96)=0.025

    Z<1.96 becomes:

    X-16<1.96 \times 0.8

    or:

    X<16+ 1.96 \times 0.8

    CB
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