To correctly label the population of 100 seeds for the purpose of taking a simple random sample, we need to choose the right range that provides a unique number to each of the 100 seeds.
Here's a step-by-step process to determine the correct labeling:
1. Define the total population size:
- The farmer has planted 100 seeds. Therefore, we need 100 unique labels to assign to each seed.
2. Determine the range:
- The range must cover 100 unique numbers to label each of the 100 seeds.
3. Possible options for labeling:
- 00-99: This represents numbers starting from 00 up to 99. This gives us 100 unique labels because it includes both the numbers 00 and 99. The total count is [tex]\( 99 - 00 + 1 = 100 \)[/tex] labels.
- 01-99: This starts at 01 and ends at 99 which gives us [tex]\( 99 - 01 + 1 = 99 \)[/tex] labels. This does not cover the entire population since we have only 99 labels for 100 seeds.
- [tex]$0-99$[/tex]: Interpreted similarly to 00-99, this covers numbers from 0 to 99, which gives us [tex]\( 99 - 0 + 1 = 100 \)[/tex] labels. Thus, it provides 100 unique labels.
- [tex]$1-100$[/tex]: This starts at 1 and ends at 100, which gives us [tex]\( 100 - 1 + 1 = 100 \)[/tex] labels. This also covers the entire population with 100 unique labels.
4. Comparison and Selection:
- Both 00-99 and [tex]$0-99$[/tex] provide 100 unique labels starting from zero.
- [tex]$1-100$[/tex] also provides 100 unique labels but starts from one.
- 01-99 provides only 99 unique labels, which is insufficient for 100 seeds.
So, the correct choices that can be used to label the population are 00-99 and [tex]$0-99$[/tex].
Out of the given options, "00-99" correctly labels the population of 100 seeds. Thus, the correct answer is:
- 00-99
