1. The problem is to calculate the three-sigma control limits for a process with mean $\bar{x} = 400$ and standard deviation $\sigma = 1.2649$. 2. The Upper Control Limit (UCL) is calculated as: $$\text{UCL} = \bar{x} + 3\sigma = 400 + 3(1.2649) = 400 + 3.7947 = 403.79$$ 3. The Lower Control Limit (LCL) is calculated as: $$\text{LCL} = \bar{x} - 3\sigma = 400 - 3(1.2649) = 400 - 3.7947 = 396.21$$ 4. These control limits mean that if any sample mean falls outside the range $396.21$ to $403.79$, the process should be flagged as out of control. Final answer: - Upper Control Limit (UCL) = 403.79 - Lower Control Limit (LCL) = 396.21