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Math Help - normal distribution problem: conditional probability

  1. #1
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    normal distribution problem: conditional probability

    If X is N(75,100), compute the conditional probability P(PX>85|X>80)

    I use the theorem sigma((b-mean)/standard deviation)-sigma((a-mean)/standard deviation) and a normal distribution probability table to get these probabilities:

    .8413 for X > 85
    and
    .6915 for X > 80.

    I see the probability of an event A given an event B has occurred is

    P(A|B)=P(A union B)/P(B)

    how could i find P(A union B) so i can apply this formula? Thanks!
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  2. #2
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    Quote Originally Posted by Evan.Kimia View Post
    If X is N(75,100), compute the conditional probability P(PX>85|X>80)
    P(A|B)=P(A union B)/P(B)

    how could i find P(A union B) so i can apply this formula? Thanks!
    It is not union. It is intersection.

    P(A|B)=\dfrac{P(A\cap B)}{P(B)}

    Hint (X>85)\cap(X>80)=(X>85)
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  3. #3
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    if I understand Plato correctly (which i probably didnt) , P(A∩B) where in this case P(A)=.8413 and P(B)=.6915, would be equal to P(A).

    but that would mean .8413/.6915 which doesnt give me the correct answer. (answer in the back of the book is .514)

    What am i missing? Thank ya.
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  4. #4
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    Quote Originally Posted by Evan.Kimia View Post
    if I understand Plato correctly (which i probably didnt) , P(A∩B) where in this case P(A)=.8413 and P(B)=.6915, would be equal to P(A).

    but that would mean .8413/.6915 which doesnt give me the correct answer. (answer in the back of the book is .514)

    What am i missing? Thank ya.
    I don't know what you are missing.
    I do know that I do not get those same numbers.
    I do know that the answer to the question you posted is \dfrac{P(X>85)}{P(X>80)}.

    Post script: Now I do get your textbook's answer.
    I was not use to the notation you are using.
    i.e. \sigma=10
    Last edited by Plato; March 26th 2011 at 03:17 PM.
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  5. #5
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    I also somehow got the wrong values out of the table for P(A) and P(B) so you were correct after all. Thanks again!
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