[klysm]

Gaussian distributions are a horrible choice for representing measurement uncertainty. If the tool is properly calibrated, 100% of the probability mass will be within (6.9, 7.1). A normal distribution would have probability mass in negative numbers!

There's also no motivation for choosing a normal distribution here - why would we expect the error to be normal?

[tlb]

If the error is the sum of many little errors, as it often is in mechanical assemblies, it's approximately normal due to the central limit theorem.

[klysm]

True, but that’s not how most sensors actually work. For example consider a weighing scale. If it says 10.1kg, why would we use a normal distribution?