Problem with amplifying a pressure sensor for measuring blood pressure

Words can be such a pain. Lower tolerance is the opposite of +/- smaller percent. Did you really mean that using a lower tolerance resistor made it work when the higher tolerance resistor did not? If so then the resistance you really want is not the one calculated but closer to what the LT resistor actually is.

A 5% tolerance resistor is higher tolerance than a 10% tolerance resistor. The higher the tolerance, the higher the accuracy must be to pass. It's intuitive if you make things to tolerances but otherwise not.

I think that they test the things every so many and if within 10% then that part of the run goes in the 10% bin even as the process is tweaked for higher accuracy. Still there's nothing saying that +/- 10% can't be within 1%, just that's not likely given consistent manufacture.