# The weights of a certain brand of candies are normally distributed with a mean weight of 0.8563 g and a standard deviation of 0.052 g. A sample of these candies came from a package containing 456 ​candies, and the package label stated that the net weight is 389.7 g.​ (If every package has 456 ​candies, the mean weight of the candies must exceed StartFraction 389.7 Over 456 EndFraction equals0.8545 g for the net contents to weigh at least 389.7 ​g.) a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8545 g. The probability is nothing. ​(Round to four decimal places as​ needed.) b. If 456 candies are randomly​ selected, find the probability that their mean weight is at least 0.8545 g. The probability that a sample of 456 candies will have a mean of 0.8545 g or greater is nothing. ​(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, No, because the probability of getting a sample mean of 0.8545 g or greater when 456 candies are selected ▼ is is not exceptionally small.

Question
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8563 g and a standard deviation of 0.052 g. A sample of these candies came from a package containing 456 ​candies, and the package label stated that the net weight is 389.7 g.​ (If every package has 456 ​candies, the mean weight of the candies must exceed StartFraction 389.7 Over 456 EndFraction equals0.8545 g for the net contents to weigh at least 389.7 ​g.) a. If 1 candy is randomly​ selected, find the probability that it weighs more than 0.8545 g. The probability is nothing. ​(Round to four decimal places as​ needed.) b. If 456 candies are randomly​ selected, find the probability that their mean weight is at least 0.8545 g. The probability that a sample of 456 candies will have a mean of 0.8545 g or greater is nothing. ​(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, No, because the probability of getting a sample mean of 0.8545 g or greater when 456 candies are selected ▼ is is not exceptionally small.