Final answer:
The question involves the concept of random sampling in statistics, where a subset of parts is randomly selected to represent a larger population for the purpose of quality control or statistical analysis.
Step-by-step explanation:
The question seems to be related to the concept of random sampling in statistics, a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of masses of numerical data. In the context provided, a student or researcher is taking a random sample of parts, likely to assess quality control or defects in a manufacturing process, or to perform statistical analysis.
Random sampling is used to obtain a representative subset of the entire population being studied so that the characteristics of the sample will approximate those of the population. There are various methods of random sampling, including simple random sampling, stratified sampling, systematic sampling, cluster sampling, and convenience sampling. Each method has its advantages and is chosen based on the specific situation and the research question.
For example, if a company produces batches of parts and wants to ensure consistent quality, they might use systematic random sampling, as suggested in point 15, where every tenth item is checked. If the company wants to ensure representation across different production lines or batches, they could use stratified sampling, as in point 14, where groups are randomly chosen. The examples provided from the question indicate different scenarios where random sampling is utilized for various research purposes.