Boxes are labeled as containing 500g of cereal. The machine filling the boxes produce weights that are normally distributed with standard deviation 12g.

Question

1) Suppose a law states that no more than 5% of a manufacturer's cereal boxes can contain less than the stated weight of 500 g. At what target weight should the manufacturer set its filling machine?
2) If (mew sign, mean symbol) is 500.8%, weigh more than y amount of grams)

Answer 1

I think you will be able to answer these questions if you play around a bit at

http://davidmlane.com/hyperstat/z_table.html