Final answer:
Stratified sampling would be the most appropriate method for the manufacturer to implement better quality-control procedures.
Step-by-step explanation:
The most appropriate sampling method for the manufacturer to implement better quality-control procedures would be stratified sampling. This method involves dividing the population into distinct groups or strata and then randomly selecting samples from each stratum.
In this case, the tool centers can be considered as separate strata. The manager can randomly select a certain number of tools from each tool center to ensure representation from all centers in the sample. This approach allows for a more accurate assessment of the quality of tools produced at each center.