Final answer:
Standard deviation measures the precision of a machine tool's output. A machine tool with a standard deviation of 0.55 would be more precise than one with a standard deviation of 0.86, but standard deviation alone does not indicate accuracy. Additional information such as the mean or target values is required to assess both precision and accuracy.
Step-by-step explanation:
The student's question seems to be asking for practical examples where a machine tool yields a certain standard deviation in its manufacturing output. Each machine tool would be assessed on its performance, specifically its precision and accuracy, which are determined by measures such as the standard deviation.
a) A machine tool with a standard deviation of 0.55 suggests that the measurements are clustered around the mean but does not indicate whether the mean is the target or desired value. Therefore, it could be precise (consistency in measurements) but possibly inaccurate (mean is far from the target).
b) A machine tool with a standard deviation of 0.86 indicates less precision as the measurements are more spread out from the mean, potentially leading to both inaccuracy and imprecision.
c) Both machine tools have standard deviations distinct from one another, and without additional context such as the mean or the target values, we cannot determine the accuracy of the tools. Standard deviation alone only informs us about the precision of the measurements.
Example Scenario: If a plant manager finds that the standard deviation of the weight of cereal boxes being filled is higher than the acceptable range, it would imply the machine tool is imprecise and might need recalibration.