Math Help - Combined Uncertainties

1. Combined Uncertainties

I am looking for some help with a very basic problem. There are three devices used for measuring volume. Device A and Device B measure volumes separately that are then combined and measured by Device C. Device A and B measure with a relative uncertainty of +- 5% with a 90% confidence interval. Device C measures with a relative uncertainty of +- 4% with a 90% confidence interval. When comparing the results from A + B with C what is the acceptable deviation? How far off can A+B be from C while still within tolerance. Thanks for any help in advance.

2. Originally Posted by Kostya
I am looking for some help with a very basic problem. There are three devices used for measuring volume. Device A and Device B measure volumes separately that are then combined and measured by Device C. Device A and B measure with a relative uncertainty of +- 5% with a 90% confidence interval. Device C measures with a relative uncertainty of +- 4% with a 90% confidence interval. When comparing the results from A + B with C what is the acceptable deviation? How far off can A+B be from C while still within tolerance. Thanks for any help in advance.
The error from the average of A and B is $\pm 5/\sqrt{2}\ \%$, the error of the difference of this average from C is $\pm \sqrt{(5/\sqrt{2})^2+4^2}\ \%$.

But you really need to consult your notes to know why.

CB