A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 lb, the boat was rated to carry 70 passengers (so the load limit was 9,310 lb). After the boat sank, the assumed mean weight for similar boats was changed from 133 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 174.4 lb and a standard deviation of 35.5 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 133 lb. The probability is 1. (Round to four decimal places as needed.) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,907 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 2,907 lb). The probability is (Round to four decimal places as needed.)