What is this the name of this statistical method?

If I take multiple readings and average them, I can get finer resolution with a certain confidence limit.
For example if I want to know the diameter of a coin to 0.001 inches and only have a ruler labeled in inches, I can randomly drop the coin on the ruler 1000 times and count the number of times it lands on an inch mark. If the coin is exactly ½ inch I can expect to see it land on the line about 500 times within a certain gaussian distirbution. If the coin landed on the line 739 times for example, I can say that I am 95% confident that the coin is .739 inches.
What is this method called?
This is driving me crazy. Thanks!