Duck Tours, Inc., runs the amphibious "duck boats" that allow visitors to Boston to view the city from the street, the river, and the harbor. Currently, each duck boat has a maximum capacity of 5000 pounds or 20 passengers. For this problem, assume that the weights in pounds of adult males, M, are normally distributed with mean AM = 195 and standard deviation oM = 30, and the weights in pounds of adult females, F, are normally distributed with mean uF = 169 and standard deviation oF = 20. the weights in pounds of children, C, are normally distributed with mean Hc = 70 and standard deviation oc = 10. 4. (15 points) Duck Tours would also like to investigate the same questions but where "worst case scenario" is replaced with "likely passenger mix". Historical data shows that adult males typically comprise 37% of each tour, adult females 44%, and children 19%. Under these assumptions about passenger mix, generate simulated boat loading scenarios assuming between 20 and 30 passengers. For each number of passengers between 20 and 30, you should generate enough scenarios to compute a simulated probability of overloading. Using the probabilities obtained from the simulated boat loading scenarios, does your recommendation about the number of passengers/boat change? How sensitive are the simulated probabilities to the proportions of adult males, adult females, and children? Investigate at least one class of passengers assuming that the proportion is 10% lower or higher than the historical data suggests.