Kola produces six-packs of soda bottles. Each bottle is supposed to contain at least 20 ounces of soda. If the total weight in a six-pack is under 120 ounces, Kola is fined $100 and receives no sales revenue for the six-pack. Each six-pack sells for $9.00. It costs Kola $0.02 per ounce of soda put in the bottles. Assume the amount put in the i-th bottle by a machine is given by Xi = µ + 0.1Yi , i = 1, … ,6, where µ is the mean fill rate of Kola’s soda-filling machines, and Y1, … , Y6 are independent standard normal random variables. Run simulations with mean fill rate µ from 20.00-20.50 in increments of 0.05. Find the mean and standard deviation of the expected profit per six-pack for each simulation. Which of the filling quantity results in the highest expected profit per six-pack?