The average demand for flu vaccines in the US for next season is $80$ million with a standard deviation of $8$ million, assume a normal distribution. Each flu vaccine costs approximately $$35$ to produce and ship to all the states. If a person wanted a vaccine and cannot not get it the estimated cost to society is $$500($this is the weighted average cost $-$ some people may still be perfectly healthy while others may require hospitalization while a few may die$).$ How many flu vaccines should the US prepare for next season? Keep in mind that when the flu season hits, it is too late to produce any additional vaccines, and that left$-$over vaccines are worthless since the flu next year will be different.

Hint: Treat this just like you would if were "selling" the vaccine $($for $$500),$ with it having cost you $$35.$ The only difference is that rather than receiving cash of $$500$ upon vaccinating someone, you are avoiding a $$500$ payout $($but you had to spend the $$35$ to save the $$500$ so the net gain, i$.$e$.,$ the cost of underage, is $$465).$

Find Cu and Co and then use the graph from a previous problem to find the z$-$score. Then add z$*$sigma to the expected demand.

Group of answer choices

$92\mathrm{.}1$

$80$ million

$68$ million

$91\mathrm{.}8$ million