Currently, quarters have weights that are normally distributed with a mean of 5.670 grams and a standard deviation of 0.062 gram. A vending machine is configured to accept only those quarters with weights between 5.550 grams and 5.790 grams.
a. If 280 different quarters are inserted into the vending machine, what is the expected number of rejected quarters?
b. If 280 different quarters are inserted into the vending machine, how likely is it that the mean falls between the limits of 5.550 grams and 5.790 grams?
c. If you owned the vending machine, which result would concern you more: the result in part a or the result in part b? Why?