The historical returns for two investments A and B are summarized in the following table for the period $2016$ to $2020$ Use the data to answer the questions that follow.

ControlA

Year Rate of Return

$201622\mathrm{.}4\%12\mathrm{.}7\%$

$20174\mathrm{.}6\%14\mathrm{.}9\%$

$201814\mathrm{.}7\%18\mathrm{.}0\%$

$201929\mathrm{.}3\%19\mathrm{.}0\%$

$202014\mathrm{.}5\%20\mathrm{.}9\%$

Average $17\mathrm{.}1\%17\mathrm{.}1\%$

a$.$ On the basis of a review of the return$$ data, which investment appears to be more$$ risky? Why?

b$.$ Calculate the standard deviation for each$$ investment's returns.

c$.$ On the basis of your calculations in part b$,$ which investment is more$$ risky? Compare this conclusion to your observation in part a$.$

Question content area bottom

A$.$

Investment A and investment B have equal risk because the average returns are the same.

B$.$

The riskier investment appears to be investment$$ B$,$ with returns that are closer to the average relative to investment$$ A$,$ whose returns are farther from the average.

C$.$

The riskier investment appears to be investment$$ A$,$ with returns that vary widely from the average relative to investment$$ B$,$ whose returns show less deviation from the average.

This is the correct answer.

D$.$

The riskier investment appears to be investment$$ B$,$ with returns that vary widely from the average relative to investment$$ A$,$ whose returns show less deviation from the average.

Part $2$

b$.$ The standard deviation for investment A is $9\mathrm{.}30\%$

Part $3$

The standard deviation for investment B is $.....\%.($Round to two decimal$$ places.$)$