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Math Help - Difficult Normal Distribution question

  1. #1
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    Smile Difficult Normal Distribution question

    X is normally distributed with mean \mu where the mean is greater than zero
    If Pr(a>X)=0.025
    what is the closest decimal approximation for the value
    Pr(-a<X<\mu)???
    a:0.025
    b:0.05
    c:0.475
    d:0.4875
    e:-0.025 (obviously wrong choice, just provided for question completeness)
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Difficult Normal Distribution question

    I would rewrite the probability:
    P(-a<X<\mu)=P(X<\mu)-P(X<-a)
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  3. #3
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    Re: Difficult Normal Distribution question

    This looks like a good approach, except how do I find Pr(x<-a)? Pr(X< mu) is obviously 0.5, but this alone doesn't allow me to solve the question...?
    Thanks in advance.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Difficult Normal Distribution question

    Notice P(X<-a)=P(X>a)=1-P(X<a)
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  5. #5
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    Re: Difficult Normal Distribution question

    This approach gives the answer as c above, but how does P(x<-a)=P(x>a) hold true even when mean is not zero?
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Difficult Normal Distribution question

    Because the graph of normal distribution is symmetric.
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  7. #7
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    Re: Difficult Normal Distribution question

    Symmetric about the mean, hence P(X<mu-b) would be equal to P(X>mu+b) for any b but if mu is not zero then P(x<-b) would not equal P(x>b) for an b. Or is there a flaw in this logic? Hmmm...
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