A boat capsized and sank in a lake. Based on an assumption ofa mean weight of 148 lb, the boat was rated to carry 60 passengers (so the load limit was 8,880 lb). After the boat sank, the assumed mean weight for similar boats was changed from 148 lb to 170 lb. Complete parts a and b below. (3 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 182.3 lb and a standard deviation of 35.2 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 148 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 2,890 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 2,890 lb). The probability is D. (Round to four decimal places as needed.) The weights of a certain brand of candies are normally distributed with a mean weight of 0.8545 g and a standard deviation of 0.0513 g. A sample of these candies came from a package containing 440 candies, and the package label stated that the net weight is 375.6 g. (If every package has 440 candies, the mean weight of the candies must 375.6 440 exceed = 0.8537 g for the net contents to weigh at least 375.6 g.) (E a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8537 g. The probability is 0.5062 . (Round to four decimal places as needed.) b. lf440 candies are randomly selected, find the probability that their mean weight is at least 0.8537 g. The probability that a sample of 440 candies will have a mean of 0.8537 g or greater is D. (Round to four decimal places as needed.) A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 201 lb and a standard deviation of 41 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 lb. Complete parts (a) through (d) below. (I) a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the gondola is lled to the stated capacity of 25 passengers? The maximum mean weight is 150 lb. {Type an integer or a decimal. Do not round.) b. If the gondola is lled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part (a)? The probability is D. (Round to four decimal places as needed.) Assume that females have pulse rates that are normally distributed with a mean of u = 76.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. . . . a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 72 beats per minute and 80 beats per minute. The probability is 0.2510 . (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean between 72 beats per minute and 80 beats per minute. The probability is (Round to four decimal places as needed.)Assume that females have pulse rates that are normally distributed with a mean of u = 75.0 beats per minute and a standard deviation of o = 12.5 beats per minute. Complete parts (a) through (c) below. . . a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 81 beats per minute. The probability is 0.6844 . (Round to four decimal places as needed.) b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 81 beats per minute. The probability is (Round to four decimal places as needed.)