A boat capsized and sank in a lake. Based on an assumption of a mean weight of 144 lb, the boat was rated to carry 70 passengers (so the load limit was 10,080 lb). After the boat sank, the assumed mean weight for similar boats was changed from 144 lb to 174 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 177.7 lb and a standard deviation of 40.5 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 144 lb. The probability is 1. (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 2,958 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,958 lb). The probability is 0.6461 (Round to four decimal places as needed.) K The overhead reach distances of adult females are normally distributed with a mean of 205.5 cm and a standard deviation of 8.3 cm. a. Find the probability that an individual distance is greater than 218.90 cm. b. Find the probability that the mean for 15 randomly selected distances is greater than 204.20 cm. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? a. The probability is 0.0537. (Round to four decimal places as needed.) b. The probability is 0.7258 (Round to four decimal places as needed.)