A boat capsized and sank in a lake. Based on an assumption of a mean weight of 145 lb, the boat was rated to carry 70 passengers(so the load limit was 10,150 lb). After the boatsank, the assumed mean weight for similar boats was changed from 145 lb to 175 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 178.7 lb and a standard deviation of 35.1 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 145 lb.

The probability is

(Round to four decimal places asneeded.)