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Math Help - normal distribution question

  1. #1
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    normal distribution question

    Consider a normally distributed random variable where mu = std. dev = k.
    Find Pr(Z > 2k):

    No idea on this one.
    (the answer is 0.1587 for reference)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    Consider a normally distributed random variable where mu = std. dev = k.
    Find Pr(Z > 2k):

    No idea on this one.
    (the answer is 0.1587 for reference)
    For clarification do we have:

    X~N(k,k^2)

    Z=(X-k)/k

    find Pr(Z>2k)?

    or:

    X~N(k,k^2)

    find Pr(X>2k)?

    If the last of these is what is intended then set

    Z=(X-k)/k,

    then Z~N(0,1)

    and

    Pr(X>2k)=Pr(Z>1)

    which can be looked up in a standard normal table.

    RonL
    Last edited by CaptainBlack; October 4th 2006 at 03:17 AM.
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  3. #3
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    im not exactly sure, the question did not say that Z was a standard normal variable, only that is was normal. But the letter Z usually denotes a std normal variable...

    Im not exactly sure how you got Pr(X>2k)=Pr(Z>1), could you clarify?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    im not exactly sure, the question did not say that Z was a standard normal variable, only that is was normal. But the letter Z usually denotes a std normal variable...

    Im not exactly sure how you got Pr(X>2k)=Pr(Z>1), could you clarify?
    If X~N(k,k^2), then if we change to Z-scores:

    z=(x-mean(x))/sd(x)=(x-k)/k

    then X>2k is equivalent to X-k>k, which is equivalent to (X-k)/k>1.

    Now Z~N(0,1),

    and Pr(Z>1)=0.1587

    RonL
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