Answer to Question #22074 in Calculus for ybot

Question

Supose we already know that heads have a defect that favour its hits.
We have tested that the coin is not fair and it is biased to heads.
Or we have modified the coin with the purpose to have an advantage.
What I want to know is the degree of deviation of this coin.
It is not the same situation being biased hitting 51/100 than hitting 55/100 or 65/100.
For all these posible conclusions we have to throw the coin x times.
In this situation we donnot need to decide wether the coin is biased or not.
Is there a degree of error to decide for example that the coin is biased to heads from 1 to 3%? Or 4 to 6% or whatever.
What are the smallest samples to determine this degree?
Is there a rule to relate the standard deviation number gained, the extension of the sample and the mean(the advantage, more than 50/100) of heads.