Quarters are now manufactured so that they have a mean weight of 5.670 g and a standard deviation of 0.062 g, and their weights are normally distributed. A vending machine is configured to accept only those quarters that weigh between 5.550 g and 5.790 g.
a. If 1 randomly selected quarter is inserted into the vending machine, what is the probability that it will be accepted?
b. If 4 randomly selected quarters are inserted into the vending machine, what is the probability that their mean weight is between 5.550 g and 5.790 g?
c. If you own the vending machine, which result is more important: the result from part (a) or part (b)?