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Math Help - SD and Normal Approximation-2

  1. #1
    Yan
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    SD and Normal Approximation-2

    Suppose the average family income in an area is $10,000.

    a) Find an upper bound for the percentage of families with incomes over $50,000.

    b)Find a better upper bound if it is known that the standard deviation of incomes is $8000.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Yan View Post
    Suppose the average family income in an area is $10,000.

    a) Find an upper bound for the percentage of families with incomes over $50,000.
    For this assume that familiea have either zero income or an income of \$ 50001. then the mean income is:

    p \times 50001 =10000

    and solve for p.


    b)Find a better upper bound if it is known that the standard deviation of incomes is $8000.
    Use the one sided Chebyshev inequality (it can be found here about two thirsd of the way down)

    CB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    For this assume that familiea have either zero income or an income of \$ 50001. then the mean income is:

    p \times 50001 =10000

    and solve for p.
    We have 50001 here because we assume that income is discrete and is an integer a number of dollars, and so $50001 is the smallest possible income in excess of $50000.

    CB
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