How to find the standard error of a sample of measurements each with their own uncertainity

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.

• According to the spec, it's 48g max and typically 45.6g. Don't expect a better precision on 3 points. – user226604 Apr 23 at 8:34
• Thanks for such a quick reply! I was going to take more measurements however I was wanting to understand the process of calculating uncertainty before going ahead and taking hundreds of measurements. How would you find the uncertainty? – Shella Apr 23 at 9:22