The weights of a certain brand of candies are normallydistributed with a mean weight of0.8612g and a standard deviationof 0.0514g. A sample of these candies came from a packagecontaining 452 candies, and the package label stated that the netweight is 385.9g.​ (If every package has452candies, the mean weightof the candies must exceed 385.9 Over 452 =0.8538g for the netcontents to weigh at least 385.9
​g.)a. If 1 candy is randomly​ selected, findthe probability that it weighs more than
0.8538
g.The probability is
​(Round to four decimal places as​ needed.)
b. If 452candies are randomly​ selected, findthe probability that their mean weight is at least 0.8538g.Theprobability that a sample of
452candies will have a mean of 0.8538g or greater is
(Round to four decimal places as​ needed.)
c. Given these​ results, does it seem that thecandy company is providing consumers with the amount claimed onthe​ label?
â–¼
No,
Yes,
because the probability of getting a sample mean of
0.8538
g or greater when
452
candies are selected
â–¼
is not
is
exceptionall small
