A boat capsized and sank in a lake. Based on an assumption of mean weight of 139 lb, the boat was rated to carry 60 passengers(so the load limit was 8,340 lb). After the boatsank, the assumed mean weight for similar boats was changed from 139 lb to 170 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 178.4 lb and a standard deviation of 36.9 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 139 lb.

The probability is ______________ (round to four decimal place as needed)

b. The boat was later rated to carry only 15 passengers, and the load limit was changed to 2,550 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170 (so that their total weight is greater than the maximum capacity of 2,550 lb).

The probability is _________ (Round to four decimal places asneeded.)

Do the new ratings appear to be safe when the boat is loaded with 15 passengers? Choose the correct answer below.

A.

Because 178.4 is greater than 170, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.

B.

Because there is a high probability ofoverloading, the new ratings do not appear to be safe when the boat is loaded with 15 passengers.

C.

Because there is a high probability ofoverloading, the new ratings appear to be safe when the boat is loaded with 15 passengers.

D.

Because the probability of overloading is lower with the new ratings than with the oldratings, the new ratings appear to be safe.