I have a scale that has a resolution of +-0.01 grams. I have assumed that it has a standard error of +-0.005 grams. I would like to measure the mass of an Samsung INR18650-30Q battery. I would like to estimate the average battery's weight because I am building a battery pack with a couple of thousand of these battery cells. I have measured three of them and their measurements are as follows...
1) 46.08 +-0.005 grams
2) 45.99 +-0.005 grams
3) 45.96 +-0.005 grams
How would I find the mean and standard error of the population given that each measurements has an uncertainty of +-0.005 grams?
------- What I've done so far --------
I have found the standard deviation which is 0.06245 (4 sf) and calculated the standard error using
SE=(standard deviation)/SQRT(Number of samples) which gives an SE of 0.0361 (4 sf).
I've also found the error propagation of averaging three measured values.
SE_P=SQRT(3*(0.005)^2)/3 which is 0.002887 (4 sf).
How can I combine the uncertainty that exists in the manufacture of each battery and the uncertainty of my scale?
I found this post but I'm not sure if it answers my question, as it finds the standard error when another measurement is made.
Let me know if you need anymore information.