Final answer:
The first three items selected for examination using systematic selection with the given parameters would be the 10th, 15th, and 20th items in the population.
Step-by-step explanation:
If systematic selection is used with a starting point of 10, a population size of 100, and a necessary sample size of 20, we first need to determine the sampling interval (also known as the sampling ratio). The sampling interval is calculated by dividing the population size by the required sample size. In this case, the interval would be 100 divided by 20, which equals 5.
Starting at the initial point of 10, we would select every 5th element from this starting point. Therefore, the first item selected would be the 10th item. To identify the next two items, we would add the sampling interval of 5 to the starting point and subsequent selections.
The first three items selected would be:
- 10th item
- 15th item (10 + 5)
- 20th item (15 + 5)