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Math Help - Last Probability Question!

  1. #1
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    Last Probability Question!

    Sorry for all the questions,
    I've been having trouble with these homework questions all week.

    Heres the last question:

    μ: $60k
    σ: $5k

    Assume that for the standard normal population the probability to not exceed 1.960 is 0.975

    A.) Find the value V such that 97.5% of households have the income above (greater than V)

    B.) Find the value U such that 2.5% of households have the income below (less than) U

    C.) What is the proportion of households with the annual income between U and V

    I have tried this a couple times, but everytime I check the answer it comes out wrong

    Any help would be greatly appreciated
    Thanks
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  2. #2
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    Quote Originally Posted by JohhnySD View Post
    Sorry for all the questions,
    I've been having trouble with these homework questions all week.

    Heres the last question:

    μ: $60k
    σ: $5k

    Assume that for the standard normal population the probability to not exceed 1.960 is 0.975

    A.) Find the value V such that 97.5% of households have the income above (greater than V)

    B.) Find the value U such that 2.5% of households have the income below (less than) U

    C.) What is the proportion of households with the annual income between U and V

    I have tried this a couple times, but everytime I check the answer it comes out wrong

    Any help would be greatly appreciated
    Thanks
    A.) Pr(X > v) = 0.975 => Pr(X < v) = 0.025 => Pr(X > -v) = 0.025 => Pr(X < -v) = 0.975.

    But Pr(Z < 1.960) = 0.975 (given) and Z = \frac{X -\mu}{\sigma} \Rightarrow 1.960 = \frac{-v - 60}{5} \Rightarrow v = ....

    You can do the others. Given the definitions of u and v in A.) and B.) I would have thought the the answer to C.) is obvious.
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