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, \( \mathrm{C}_{\mathrm{p}} \), we use the formula: \[ \mathrm{C}_{\mathrm{p}} = \frac{\text{Upper Specification Limit} - \text{Lower Specification Limit}}{6 \times \sigma} \] Given that the difference is 0.70 and the standard deviation \( \sigma \) is 0.10, the calculation becomes: \[ \mathrm{C}_{\mathrm{p}} = \frac{0.70}{6 \times 0.10} = \frac{0.70}{0.60} \approx 1.17 \] With a \( \mathrm{C}_{\mathrm{p}} \) of 1.17, we can confidently say that the process is capable, meaning it has a good ability to produce items within specifications. This ratio essentially means that for every 6 standard deviations, the process can fit within the specification limits. A \( \mathrm{C}_{\mathrm{p}} \) between 1.0 and 1.33 suggests a capable process, while anything above 1.33 indicates an even higher capability. So, in this case, you can consider it capable!