An archaeological wood sample is analyzed using carbon-14 dating (\(^{14}\text{C}\), half-life \(T_{1/2} = 5{,}730 \text{ years}\)). The measured activity of \(^{14}\text{C}\) per gram of carbon in the sample is found to be \(12.5\%\) of the activity measured per gram in a living organism. Which choice correctly states the estimated age of the sample and provides the correct physical justification regarding measurement uncertainty?