a. If 1 candy is randomly selected. find the probability that it weighs more than 0.8539 g. The probability is 0.5438'. (Round to four decimal places as needed.) b. If 461 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g. The probability that a sample of 461 candies will have a mean of 0.8539 g or greater is 0.9924'. (Round to four decimal places as needed.) c. Given these results, does it seem that the candy company is providing consumers with the amount claimed on the label? Yes, because the probability of getting a sample mean of 0.8539 g or greater when 461 candies are selected is not exceptionally small. The weights of a certain brand of candies are normally distributed with a mean weight of 0.8586 g and a standard deviation of 0.0518 g. A sample of these candies came from a package containing 453 candies, and the package label stated that the net weight is 386.9 g. (If every package has 453 candies, the mean weight of the candles must 386.9 453 = 0.8541 g for the net contents to weigh at least 386.9 g.) exceed 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. E) 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. lfthe 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 1 . (Round to four decimal places as needed.) c. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is lled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb? The probability is D. (Round to four decimal places as needed.) A boat capsized and sank in a lake. Based on an assumption of a mean weight of 141 lb, the boat was rated to carry 50 passengers (so the load limit was 7,050 lb). After the boat sank, the assumed mean weight for similar boats was changed from 141 lb to 172 lb. Complete parts a and b below. (1) a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 180.8 lb and a standard deviation of 39.3 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 141 lb. The probability is 1 . (Round to four decimal places as needed.) b. The boat was later rated to carry only 15 passengers, and the load limit was changed to 2,580 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 172 {so that their total weight is greater than the maximum capacity of 2,580 lb). The probability is |:|. (Round to four decimal places as needed.)