Quarters have weights that are normally distributed with a mean of 5.67 g and a standard deviation of 0.070 g.
a. If a vending machine is adjusted to reject quarters weighing less than 5.53 g or more than 5.81 g, what is the percentage of legal quarters that are rejected?
b. Find the weights of accepted legal quarters if the machine is readjusted so that the lightest 1.5% are rejected and the heaviest 1.5% are rejected.
c. If your quarter is rejected from a machine that is set to reject the upper 1.5% and the lower 1.5% of coins, by weight, is it a waste of time to reinsert your coin?