(Solved): A boat capsized and sank in a lake. Based on an assumption of a mean weight of \( 145 \mathrm{lb} \ ...

A boat capsized and sank in a lake. Based on an assumption of a mean weight of \( 145 \mathrm{lb} \), the boat was rated to carry 60 passengers (so the load limit was \( 8,700 \mathrm{lb} \) ). After the boat sank, the assumed mean weight for similar boats was changed from \( 145 \mathrm{lb} \) to \( 172 \mathrm{lb} \). Complete parts a and b below. 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 \( 179.9 \mathrm{lb} \) and a standard deviation of \( 37.7 \mathrm{lb} \). Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than \( 145 \mathrm{lb} \). The probability is (Round to four decimal places as needed.)