$5.$ Suppose Ann has the following utility function, U $=3$W $0\mathrm{.}3$

Ann is considering an investment in a business which would yield $$6,400$ with probability $1$

$5,$

and $$3,600$ with probability $4$

$5$

a$.$ What is the expected value, variance, and standard deviation of this business investment?

b$.$ What is Ann$$s expected utility from this business investment?

c$.$ Suppose the cost of the business investment was $$4,000.$ Should Ann make this investment?

Support your answer using expected utility theory.

d$.$ What is Ann$$s Arrow$-$Pratt measure of absolute risk aversion? What type of risk$-$preferences

does Ann have $($assume W is positive$)?$