A boat capsized and sank in a lake. Based on an assumption of a mean weight of 130 lb, the boat was rated to carry 70 passengers (so the load limit was 9, 100 lb) After the boat sank, the assumed mean weight for similar boats was changed from 130 lb to 171 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 178.8 lb and a standard deviation of 40.9 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 130 lb. The probability is (Round to four decimal places as needed.)