The trial of the pyx. In 1150, it was recognized in England that coins should have a standard weight of precious metal as the basis for their value. A guinea, for example, was supposed to contain 128 grains of gold. (There are equivalent to the sum having a standard deviation of about 9 grains.

a) In effect, the trial of the pyx required that the mean weight of the sample of 100 coins have a standard deviation of 0.09 grains. Explain what was wrong with performing the trial in this manner.

b) What should the limit have been on the standard deviation of the mean?

Note: Because of this error, the crown was exposed to being cheated by private mints that could mint coins with greater variation and then, after their coins passed the trial, select out the heaviest ones and recast them at the proper weight, retaining the excess gold for themselves. The error per- sisted for over 600 years, until sampling distributions became better understood.