Do bonds reduce the overall risk of an investment portfolio? Let $x$ be a random variable representing annual

percent return for Vanguard Total Stock Index $($all stocks$).$ Let y be a random variable representing annual

return for Vanguard Balanced Index $(60\%$ stock and $40\%$ bond$).$ For the past several years, we have the

following data.

$x$ data:

y data:

$15$

$8$

$21$

$10$

$0$

$7$

$9$

$9$

$21$

a$)$ Find the sample mean, variance, and standard deviatino for $x$ and $y.($Round your answers to two decimal

places.$)$ b$.)$ Compute a $75\%$ Chebyshev interval around the mean for $x$ values and also for $y$ values. $($Round your answers to two decimal places.$)$

$\backslash$table$[[,$x$,$y$],[$Lower limit$,,],[$Upper limit$,,]]$

Use the intervals to compare the two funds.

$25\%$ of the returns for the balanced fund fall within a narrower range than those of the stock fund.

$75\%$ of the returns for the balanced fund fall within a narrower range than those of the total stock fund.

$25\%$ of the returns for the total stock fund fall within a wider range than those of the balanced fund.

$75\%$ of the returns for the total stock fund fall within a narrower range than those of the balanced fund.

c$)$ Compute the coefficient of variation for each fund. $($Round your answer to the nearest percent.$)$

$\begin{array}{cc}CV\text{f}\text{o}\text{r}x& \%\\ CV\text{f}\text{o}\text{r}y& \%\end{array}===$

Use the coefficients of variation to compare the two funds.

For each unit of return, the total stock fund has lower risk.

For each unit of return, the balanced fund has lower risk.

For each unit of return, the funds have equal risk.