Text book: Statistics for Business 2nd Edition by Robert Stine
Case: Modeling Sampling Variation based on M&M
1. M & M weigh 0.86 grams on average with SD=0.04 grams, so the coefficient of variation is 0.04/0.86=0.047. Suppose that we decided to lable packages by count rather than weight. The system adds candy to a package until the weight of the package exceeds a threshold. How large would we have to set the threshold weight to be 99.5% sure that a package has 60 pieces?
2. Suppose the same system is used (packaging by count), but this time we only want to have 10 pieces in a package. Where is the largest weight? Again we want to be 99.5% sure that the package has at least 10 pieces. What is the target weight with 99.5% surety? What assumptions are relevant to these small counts?
3. In which situation (10 pieces or 60 pieces) would the packaging system be more likely to put more than the labeled count on the candies into a Package?