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 60 passengers (so the load limit was 7,800 lb). After the boat sank, the assumed mean weight for similar boats was changed from 130 lb to 171 lb. The probability is

A. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mean of 178.3 lb and a standard deviation of 39.1 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 130 lb.

B. 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).

The probability is