A boat capsized and sank in a lake. Based on an assumption of a mean weight of 138 lb, the boat was rated to carry 70 passengers (so the load limit was 9,660 lb). After the boat sank, the assumed mean weight for similar boats was changed from 138 lb to 171 lb. Assume that the weights of people are normally distributed with a mean of 179.3 lb and a standard deviation of 35.4 lb.

The boat was later rated to carry only 16 passengers, and the load limit was changed to 2,736 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 (so that their total weight is greater than the maximum capacity of 2,736 lb).