The weights of a certain brand of candies are normally distributed with a mean weight of 0.8538 g and a standard deviation of 0.0525 g. A sample of these candies came from a package containing 470 candies, and the package label stated that the net weight is 401.0 g. (If every package has 470 candies, the mean weight of the candies must exceed 170 =0.8532 g for the net contents to weigh at least 401.0 g.) 401.0 a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g. The probability isn (Round to four decimal places as needed.) b. If 470 candies are randomly selected, find the probability that their mean weight is at least 0.8532 g The probability that a sample of 470 candies will have a mean of 0.8532 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? the prohahillitu of mean of 0 8632 a areater ubee 470 cene

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The weights of a certain brand of candies are normally distributed with a mean weight of 0.8538 g and a standard deviation of 0.0525 g. A sample of these candies came from a package containing 470 candies, and the package label stated that the net weight is 401.0 g. (If every package has 470 candies, the mean weight of the
401.0
candies must exceed 70 = 0.8532 g for the net contents to weigh at least 401.0 g.)
a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g.
The probability is N
(Round to four decimal places as needed.)
b. If 470 candies are randomly selected, find the probability that their mean weight is at least 0.8532 g.
The probability that a sample of 470 candies will have a mean of 0.8532 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 0.8532 g or greater when 470 candies are selected
exceptionally small.
Transcribed Image Text:The weights of a certain brand of candies are normally distributed with a mean weight of 0.8538 g and a standard deviation of 0.0525 g. A sample of these candies came from a package containing 470 candies, and the package label stated that the net weight is 401.0 g. (If every package has 470 candies, the mean weight of the 401.0 candies must exceed 70 = 0.8532 g for the net contents to weigh at least 401.0 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8532 g. The probability is N (Round to four decimal places as needed.) b. If 470 candies are randomly selected, find the probability that their mean weight is at least 0.8532 g. The probability that a sample of 470 candies will have a mean of 0.8532 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 0.8532 g or greater when 470 candies are selected exceptionally small.
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