>Instead of treating each as exactly 7 feet, we can instead say that each is somewhere between a minimum of 6.9 feet and a maximum of 7.1. We can write this as an interval (6.9, 7.1).
Yes we can use an interval to express an uncertainty. However, uncertainties in physical measurements are a little bit more complicated.
When I measure something to be 7 plus minus 0.1 feet, what I am saying is that the value of the measured variable is not known for sure. It can be represented by a bell curve centred on 7 and 95% of the area under the curve (95% probability) that the true value lies between 6.9 and 7.1. The value of the measured variable is much more likely to be 7 than 6.9. There is also a small chance that the value lies outside of the 6.9 to 7.1 range.
In an interval, there is no probability distribution. It is more like an infinite list of numbers.
In practice, interval arithmetic is seldom used for uncertainty analysis for scientific experiments.