12. A new water taxi has a maximal load capacity of 3,200 pounds. Adult males’ weight is normally distributed with µ = 182.5 pounds and σ = 40.8 pounds and adult females’ weight is normally distributed with µ = 165.2 pounds and σ = 45.6 pounds.

The safety certificate sets the maximum number of people at 16

(including the driver). It is not possible to know how many male and female passengers will get on the water taxi for every trip. On average, males weigh more than females. To calculate the worst case scenario (e.g., the highest probability to overload the water taxi), it is prudent to assume that all passengers and the driver are male in this calculation. What is the probability that this water taxi overloads when carrying 15 male passengers and a male driver?