A boat capsized and sank in a lake. Based on an assumption of a mean weight of 131 lb, the boat was rated to carry 60 passengers, so the load limit was 7,860 lb. After the boat sank, the assumed mean weight for similar boats was changed from 131 lb to 173 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 176.1 lb and a standard deviation of 40.2 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 131 lb.

The probability is ____. (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 2,941 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 173 lb (so that their total weight is greater than the maximum capacity of 2,941 lb).

The probability is ____. (Round to four decimal places as needed.)

Do the new ratings appear to be safe when the boat is loaded with 17 passengers? Choose the correct answer below.

A. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe.
B. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with passengers.
C. Because there is a high probability of overloading, the new ratings do not appear to be safe when the boat is loaded with 17 passengers.

Click to select your answer(s).