The weights of a certain brand of candies are normally distributed with a mean weight of 0.8548 g and a standard deviation of 0.0512 g. A sample of these candies came from a package containing 444 candies, and the package label stated that the net weight is 379.3 g. (If every package has 444 candies, the mean weight of the candies must exceed 379.3/444 = 0.8543 g for the net contents to weigh at least 379.3 g.)
(a) If 1 candy is randomly selected, find the probability that it weighs more than 0.8542g. (Round to four decimal places as needed.)
(b) If 447 candies are randomly selected find the probability that their mean weight is at least 0.8542 g. (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?