Machines used to fill food cartons are usually set to slightly overfill the boxes so that the contents will not weigh less than the advertised net weight. This takes into account the fact that the actual weight of each box varies somewhat from the machine set value. Suppose a machine is set to put 12.2 ounces of food in boxes whose advertised weight is 12 ounces, and the filling process has a distribution that is normal with a standard deviation of 0.1 ounces.
(a) What percentage of boxes would you expect to be under weight?
(b) Ninety percent of the boxes should have at least how many ounces of food?