A machine for making nuts is known to create nuts with a standard deviation in size of 0.20mm. A tradesman is required to adjust the machine to make 49mm nuts. Unfortunately the machines scale is missing and the tradesman has to adjust it by trial and error. How many nuts does he have to make and test after an adjustment before he can be certain at the 95% level of significance that the machine is calibrated to within 0.04mm of the correct size?
This is a sample size determination problem
Tolerance = 0.04mm
This post explains how to calculate the sample size required for attaining a particular level of confidence level. Explained in detail with formula and calculations.