Suppose you play a die rolling game in which a fair 6-sided die is rolled once. If the outcome of the roll (the number of dots on the side facing upward) is more than five, you win $8, otherwise you lose $2. Let X be the profit of the game or the amount of money won or lost per roll. Negative profit corresponds to lost money.

A math course has two midterms and a final exam. Midterm 1 is worth 18% of the final grade, midterm 2 is worth 36% of the final grade, and the final exam is worth 46%. The teacher assigns grades as marks on 100. If a student recieved a mark of 78.1 on the first midterm and 72.6 on the second midterm, what mark does he need on the final exam to get a final grade of 80 in the course. Please use excel for all calculations. Give the answer to 5 decimal places.