# Thread: SD and Normal Approximation-2

1. ## 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. 2. Originally Posted by Yan Suppose the average family income in an area is$10,000.

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

$\displaystyle p \times 50001 =10000$

and solve for $\displaystyle p$.

b)Find a better upper bound if it is known that the standard deviation of incomes is $8000. Use the one sided Chebyshev inequality (it can be found here about two thirsd of the way down) CB 3. Originally Posted by CaptainBlack For this assume that familiea have either zero income or an income of$\displaystyle \$50001$. then the mean income is:

$\displaystyle p \times 50001 =10000$

and solve for $\displaystyle p$.
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