De Moivre's Equation (http://math.stackexchange.com/questions/253486/name-of-de-moivres-equation)

Excerpt:

In 1150, a century after the Battle of Hastings, it was recognized that

the king could not just print money and assign to it any value he chose.

Instead the coinage’s value must be intrinsic, based on the amount of

precious materials in its makeup. And so standards were set for the

weight of gold in coins—a guinea should weigh 128 grains (there are

360 grains in an ounce). It was recognized, even then, that coinage

methods were too imprecise to insist that all coins be exactly equal

in weight, so instead the king and the barons, who supplied the London Mint (an independent organization) with gold, insisted that coins

when tested* in the aggregate [say one hundred at a time] conform

to the regulated size plus or minus some allowance for variability

[1/400 of the weight] which for one guinea would be 0.32 grains and

so, for the aggregate, 32 grains). Obviously, they assumed that variability decreased proportionally to the number of coins and not to its square root.

If the variability were too great, it would mean that there would be an unacceptably large number of too heavy coins produced that could be collected, melted down, and recast with the extra gold going into the pockets of the minter. By erroneously allowing too much variability, the Mint could stay within the bounds specified and still make extra money by collecting heavier than average coins and reprocessing them.

My Question: I am confused how assuming proportionality would allow for greater variability. The way I read the equation, if i replace the square root of n with n in the denominator I will get a smaller value and therefore my assumption of proportionality would lead to a lower allowable threshold for the aggregate weight of the coins.

I may be misunderstanding how to map the equation to this example. I was mapping 1/400 to the standard deviation of the averages of the samples.

Thanks!