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