A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 lb, the boat was rated to carry 70 passengers (so the load limit was 9,310 lb). After the boat sank, the assumed mean...

Extracted text: A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 lb, the boat was rated to carry 70 passengers (so the load limit was 9,310 lb). After the boat sank, the assumed mean weight for similar boats was changed from 133 ib to 170 1b. 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 181.5 lb and a standard deviation of 35.7 Ib. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 133 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 2,890 Ib Find the probability that the boat is overloaded because the mean welght of the passengers is greater than 170 (so that their total weight is greater than the maximum capacity of 2,890 Ib). 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. O A. Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe. O B. 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. O C. Because there is a high probability of overloading, the new ratings appear to be safe when the boat is loaded with 17 passengers O D. Because 181.5 is greater than 170, the new ratings do not appear to be safe when the boat is loaded with 17 passengers