The difference between the upper specification and the lower specification for a process is 0.70 . The standard deviation is 0.10 . Based on the given information, the process capability ratio, \( \mathrm{C}_{\mathrm{p}}= \) 1.17 (round your response to two decimal places). Based on the process capability ratio \( \left(\mathrm{C}_{\mathrm{p}}\right) \) for the given information, one can say that the process is 1 point(s) possible bery much capable not at all capable capable

To determine the process capability ratio \( \mathrm{C}_{\mathrm{p}} \) and assess the capability of the process, we can follow these steps: 1. **Extract Known Conditions:** - Difference between upper specification and lower specification: \( USL - LSL = 0.70 \) - Standard deviation: \( \sigma = 0.10 \) 2. **Calculate the Process Capability Ratio \( \mathrm{C}_{\mathrm{p}} \):** The formula for the process capability ratio is given by: \[ \mathrm{C}_{\mathrm{p}} = \frac{USL - LSL}{6\sigma} \] Substituting the known values into the formula: \[ \mathrm{C}_{\mathrm{p}} = \frac{0.70}{6 \times 0.10} \] 3. **Perform the Calculation:** - First, calculate \( 6 \times 0.10 \): \[ 6 \times 0.10 = 0.60 \] - Now, substitute this back into the equation for \( \mathrm{C}_{\mathrm{p}} \): \[ \mathrm{C}_{\mathrm{p}} = \frac{0.70}{0.60} \] 4. **Final Calculation:** \[ \mathrm{C}_{\mathrm{p}} = 1.1667 \] Rounding this to two decimal places gives: \[ \mathrm{C}_{\mathrm{p}} \approx 1.17 \] 5. **Assessing Process Capability:** - A \( \mathrm{C}_{\mathrm{p}} \) value of 1.17 indicates that the process is capable, as it is greater than 1. A \( \mathrm{C}_{\mathrm{p}} \) of 1.0 is considered the minimum acceptable level for a capable process. Based on the calculated \( \mathrm{C}_{\mathrm{p}} \) value of 1.17, we can conclude that the process is: - **Capable** Thus, the answer is: **capable**.