An experiment was conducted by weighting 20 sets of items with known quantity and the weight of items in each trail were obtained. We also know the weight of each item is supposed to be $W$ kg (however this may vary and assumed it follows normal distribution). With all this information, how can we estimate the number of items with any given weight?
I try to use simple linear regression model to first estimate $\mu$ and $\sigma^2$. I set the weight of the $i$-th trail divided by square root of number of items in the $i$-th trial equals square root of items in $i$-th trial times $\mu$ plus residual of $i$-th trial, where $i=1,...20$.
However, I do not know what should I do next since $\mu$ and all the residuals are unknown. Apart from that, the estimate of $\mu$ and $\sigma^2$ in this problem are just calculated from those 20 trials and if we do another 20 trials with same setting the outcome will probably be different. So how should I assess the behaviour or reliability of my point estimate?