Week $13-$ Chapter $09$ & Chapter $10($Up to Notes $-$ Slides Page $18)$

MC Question $1$

$($Notes $-$ Chapter $9$ Pages $4$ & $11)$

A decision analysis problem is given with three decision alternatives and three states of nature is given. The payoff is profit. For the lottery having the best payoff of $$90$ with probability $p$ and the worst payoff of $$10$ with probability $(1-p),$ it is given that $U($$$90)=9$ and $U($$$10)=1.$

If the indifference probability of $$75$ is $0\mathrm{.}9,$ find the Utility value of $$75,U($$$75).$ Correct the final answer to $2$ decimal places.

$($A$)8\mathrm{.}2$

$($B$)7\mathrm{.}4$

$($C$)5\mathrm{.}8$

$($D$)7\mathrm{.}5$

$($E$)$ None of the above