Under EU legislation on harmonization, all kippers are to weigh 0.2000 kg, and vendors who sell underweight kippers must be fined by their government. The weight of a kipper is normally distributed, with a mean of 0.2000 kg and a standard deviation of 0.0100 kg. They are packed in cartons of 100 and large quantities of them are sold.
Every day, a carton is to be selected at random from each vendor and tested according to one of the following schemes, which have been approved for the purpose.
1. The entire carton is weighed, and the vendor is fined 2500 euros if the average weight of a kipper is less than 0.1975 kg.
2. Twenty five kippers are selected at random from the carton; the vendor is fined 100 euros if the average weight of a kipper is less than 0.1980 kg.
3. Kippers are removed one at a time, at random, until one has been found that weighs more than 0.2000 kg; the vendor is fined 4 n ( n - 1) euros, where n is the number of kippers removed.
Which scheme should the Chancellor of the Exchequer be urging his government to adopt?