A flight from LA to Chicago has 100 seats. Tickets are sold at two different prices: $400 (full fare) and $120 (discount fare). The demand for discount fares follows a uniform distribution U(120, 180). The demand for full fares is estimated to be Poisson with mean 20 (the table below gives the distribution function). In addition, the airline has found that the number of people who purchased tickets but did not show up for a flight is normally distributed with mean 20 and standard deviation 10. The airline estimates that the ill will and penalty costs associated with not being able to board a passenger holding confirmed reservation are $400. x 20 21 22 23 24 25 26 27 28 29 30 Prob (Dx) 0.559 0.644 0.721 0.787 0.843 0.888 0.922 0.948 0.966 0.978 0.987 To determine the optimal protection level, what is the critical fractile