The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.0513 g. A sample of these candies came from a package containing 456 candies, and the package label stated that the net 389.4 weight is 389.4 g. (If every package has 456 candies, the mean weight of the candies must exceed - 456 = 0.8539 g for the net contents to weigh at least 389.4 g.)

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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of
0.0513 g. A sample of these candies came from a package containing 456 candies, and the package label stated that the net
389.4
weight is 389.4 g. (If every package has 456 candies, the mean weight of the candies must exceed
456
= 0.8539 g for the net
contents to weigh at least 389.4 g.)
a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8539 g.
The probability is
(Round to four decimal places as needed.)
b. If 456 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g.
The probability that a sample of 456 candies will have a mean of 0.8539 g or greater is
(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?
because the probability of getting a sample mean of 0.8539 g or greater when 456 candies are selected
exceptionally small.
Transcribed Image Text:The weights of a certain brand of candies are normally distributed with a mean weight of 0.8544 g and a standard deviation of 0.0513 g. A sample of these candies came from a package containing 456 candies, and the package label stated that the net 389.4 weight is 389.4 g. (If every package has 456 candies, the mean weight of the candies must exceed 456 = 0.8539 g for the net contents to weigh at least 389.4 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8539 g. The probability is (Round to four decimal places as needed.) b. If 456 candies are randomly selected, find the probability that their mean weight is at least 0.8539 g. The probability that a sample of 456 candies will have a mean of 0.8539 g or greater is (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? because the probability of getting a sample mean of 0.8539 g or greater when 456 candies are selected exceptionally small.
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