The following table shows the total return and the number of funds for four categories of mutual funds.

Excel File: data$03-17.$xlsx

$\backslash$table$[[$Type of Fund,Number of Funds,Total Return $(\%)],[$Domestic Equity,$9,191,4\mathrm{.}65],[$International Equity,$2,621,18\mathrm{.}15],[$Specialty Stock,$1,419,11\mathrm{.}36],[$Hybrid$,2,900,6\mathrm{.}75]]$

a$.$ Using the number of funds as weights, compute the weighted average total return for these mutual funds. $($to $2$ decimals$)\%$

b$.$ Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part $($a$)?$ Discuss. What else might be used for weights?

$($i$)$ Using "number of funds" as weights will only be a good approximation if the amount invested in various funds is approximately equal. The amount invested in each fund could be used for weights.

$($ii$)$ Using "number of funds" as weights results in a good approximation regardless of the amount invested in various funds. There is no need to use a different weight.

$($iii$)$ Using "number of funds" as weights will only be a good approximation if the amount invested in various funds is approximately equal. There is no other option that could be used for weights.

$($iv$)$ Using "number of funds" as weights results in a good approximation regardless of the amount invested in various funds. The total amount invested in all funds could be used for weights.

Choose the correct option.

Select your answer $-$ :

c$.$ Suppose you invested $$10,000$ in this group of mutual funds and diversified the investment by placing $$2,000$ in Domestic Equity funds, $$4,000$ in International Equity funds, $$3,000$ in Specialty Stock funds, and $$1,000$ in Hybrid funds. What is the expected return on the portfolio? $($to $2$ decimals$)\%$