$($Related to Checkpoint$8\mathrm{.}2)($Computing the standard deviation for an individual$$ investment$)$James Fromholtz is considering whether to invest in a newly formed investment fund. The$$ fund's investment objective is to acquire home mortgage securities at what it hopes will be bargain prices. The fund sponsor has suggested to James that the$$ fund's performance will hinge on how the national economy performs in the coming year. $$ Specifically, he suggested the following possible$$ outcomes:$$LOADING$....$

a$.$Based on these potential$$ outcomes, what is your estimate of the expected rate of return from this investment$$ opportunity?

b$.$Calculate the standard deviation in the anticipated returns found in part a$.$

c$.$Would you be interested in making such an$$ investment? Note that you lose all your money in one year if the economy collapses into the worst state or you double your money if the economy enters into a rapid expansion. State of Economy Probability Fund Returns

Rapid expansion and recovery $15\%100\%$

Modest growth $30\%30\%$

Continued recession $40\%10\%$

Falls into depression $15\%-100\%$