To determine which sample is a better representation of the actual population of the trail mix, we would need to compare the composition of Kevin's and Mark's samples to the known composition of the trail mix. A sample that closely matches the population proportions would be considered more representative.
The known population proportions are as follows:
- Peanuts: 40%
- Almonds: 40%
- Raisins: 20%
The solution requires a comparison of each person's sample to these proportions. However, since the specific compositions of Kevin's and Mark's samples are not provided, we cannot make a definitive statement about which sample is more representative.
To evaluate the representativeness of a sample, we generally look at how well the sample percentages match the known population percentages for each component.
A step-by-step approach to determining representativeness, if we were given the sample data, would be:
1. Calculate or identify the percentage of each component (peanuts, almonds, and raisins) in Kevin's sample.
2. Calculate or identify the percentage of each component in Mark's sample.
3. Compare Kevin's sample percentages to the population percentages for each component:
- A "good" representative sample will have percentages very close to 40% peanuts, 40% almonds, and 20% raisins.
4. Compare Mark's sample percentages to the population percentages for each component, using the same criteria as in step 3.
5. Determine which sample has percentages that are closer to the population percentages for each component of the trail mix.
6. Make a conclusion about which sample (Kevin's or Mark's) is a better representation, or if both are equally representative, or if neither is representative.
Without the specific compositions, we can't complete these steps, and therefore can't conclude whether Kevin's sample or Mark's sample is more representative of the actual trail mix population. Therefore, the correct answer from the choices provided would be that we cannot determine which is better without more information.
