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Accuracy is how close a measured value is to the actual (true) value.
Precision is how close the measured values are to each other.
Based on Control chart assuming X is the desired measurement level the process measurements are not accurate for sure.
Precision level can debated but since most of measurements are close to each other we can assume process is precise but its debatable as limited information is provided in the question on what is projects/organizations accepted deviation from mean
What is the source of this question? at this stage i will say that goal of this question is achieved since it made you clear about the difference between accuracy and precision. Now yes the questions has limited information and your understanding of definition is right.
For me the precise value is mean+SD 1 , so i do not take mean as precise value since most of the measurements are clustered between mean and SD 1 , since values are distributed across so it can not be accurate else we get only one value.... and the problem here is we do not know accurate value, i think you may be taking mean as accurate value but this question does not tell that.
So i can only say this is not accurate, but i can not say it is more accurate or precise ...since i do not know the right value to measure accuracy.