If these are the confidence intervals for the sample...

4470mm ± 23.86mm represents 68% of sample

4470mm ± 47.72mm represents 95% of sample

4470mm ± 71.58mm represents 99% of sample

I assume then that there is a 99% chance that the mean length of the total strings is between 4398.42mm and 4541.58mm.

But is that true for the total number of strings? or is that only true for the sample?

What do I have to do to get a similar answer as above but for the total number of strings?