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Math Help - Calculating Margin of Error Probability

  1. #1
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    Calculating Margin of Error Probability

    Here is the question:

    The monthly expenditures on food by single adults in Missoula are normally distributed with a mean of $410 and a SD of $70. What is the probability that the margin of error made in estimating the mean monthly expenditure of all single adults in that city by the mean of a random sample of 90 such adults will be at most $10?

    What I did:

    I tried using this equation, E=Z(a/2)SD/SQRT(N) => and get Z(a/2)=1.3553 which gives me a 91.15%. This seems really high though and I'm not sure what to do from here.

    Thanks!
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  2. #2
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    Quote Originally Posted by crabchef View Post
    Here is the question:

    The monthly expenditures on food by single adults in Missoula are normally distributed with a mean of $410 and a SD of $70. What is the probability that the margin of error made in estimating the mean monthly expenditure of all single adults in that city by the mean of a random sample of 90 such adults will be at most $10?

    What I did:

    I tried using this equation, E=Z(a/2)SD/SQRT(N) => and get Z(a/2)=1.3553 which gives me a 91.15%. This seems really high though and I'm not sure what to do from here.

    Thanks!
    Solve z_{\alpha/2} \frac{70}{\sqrt{90}} = 10 for z_{\alpha/2} (since it's two-sided) and hence for \alpha:

    z_{\alpha/2} = 1.3553 \Rightarrow \alpha = 2 (0.087667) = 0.18.

    So the required probability is 1 - \alpha = 0.82.
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