Snack Food Companies Always Have a Target Weight When Filling

Essay

Snack food companies always have a target weight when filling a box of snack crackers. It is not possible, however, to always fill boxes to the exact target weight. For a particular box of crackers, the target weight is 14 ounces. The filling machine drops between 13.5 and 15 ounces of crackers into each box. If these weights are uniformly distributed, what is the expected value of the fill weights? Does this value match the target weight? If not, what impact does this difference have on the manufacturer's costs to produce these crackers?