(Solution) - M M plain candies have weights that are normally distributed with -(2025 Original AI-Free Solution)

Paper Details

M&M plain candies have weights that are normally distributed with a mean weight of 0.8565 gram and a standard deviation of 0.0518 gram (based on measurements from one of the authors). A random sample of 100 M&M candies is obtained from a package containing 465 candies; the package label states that the net weight is 396.9 grams. (If every package has 465 candies, the mean weight of the candies must exceed 396.9/465 = 0.8535 for the net contents to weigh at least 396.9 grams.)
a. If 1 M&M plain candy is randomly selected, how likely is it that it weighs more than 0.8535 gram?
b. If 465 M&M plain candies are randomly selected, how likely is it that their mean weight is at least 0.8535 gram?
c. Given these results, does it seem that the Mars Company is providing M&M consumers with the amount claimed on the label?