A production process manufactures items with weights that are normally distributed with mean 15 pounds and standard deviation 0.1 pound. An item is considered to be defective if its weight is less than 14.8 pounds or greater than 15.2 pounds. Suppose that these items are currently produced in batches of 1000 units.
a. Find the probability that at most 5% of the items in a given batch will be defective.
b. Find the probability that at least 90% of the items in a given batch will be acceptable.
c. How many items would have to be produced in a batch to guarantee that a batch consists of no more than 1% defective items?