Answer:
To determine which population is the LEAST likely to have produced the given sample {40, 32, 21, 31, 24}, we need to compare the characteristics of the sample with the plotted medians of each population.
The sample consists of five data points, and we can see that the values are relatively low (ranging from 21 to 40).
Looking at the plotted medians, we can observe the following:
- The median of Population A is around 50.
- The median of Population B is around 60.
- The median of Population C is around 70.
- The median of Population D is around 80.
Since the sample values are much lower than any of the medians, it is less likely that the sample was selected from a population with a higher median value.
Therefore, we can conclude that the sample {40, 32, 21, 31, 24} is LEAST likely selected from Population D, which has the highest median value among the plotted populations.
To summarize:
- The sample is least likely selected from Population A, Population B, or Population C, as their medians are higher than the values in the sample.
- The sample is LEAST likely selected from Population D, which has a higher median value compared to the other populations.
Therefore, the answer is D. Population D is the least likely population from which the sample was selected.
