Suppose certain coins have weights that are normally distributed with a mean of 5.845 g and a standard deviation of 0.074 g. A vending machine is configured to accept those coins with weights between 5.765 g and 5.925 g.
a. If 280 different coins are inserted into the vending machine, what is the expected number of rejected coins?
b. If 280 different coins are inserted into the vending machine, what is the probability that the mean falls between the limits of 5.765 and 5.925 g?
c. Which results is more important to the owner of the vending machine? Why?