Final answer:
Both 45 and 46 are reasonable predictions for the number of country songs in 130 songs due to statistical analysis, specifically using normal distribution and confidence intervals which allow for slight variability around the sample mean. Thus, the correct option is D.
Step-by-step explanation:
Both 45 and 46 are reasonable predictions for the number of country songs played in a set of 130 songs because of statistical analysis applied to sample data. When looking at the outcomes from a sample, it is common to make predictions about the whole population. Given that the sample size is large (greater than 30), a normal distribution can be applied as an excellent approximation.
When predicting the number of country songs, knowing the average or expecting some variability allows for a range of reasonable predictions. For example, if on average, about one-third of the songs played on a station are country, then predicting that out of 130 songs, approximately 43 (which is one-third) would be country seems reasonable. Both 45 and 46 are close to this figure, hence reasonable due to potential sampling error and the understanding that in practice, these numbers would vary slightly from sample to sample.
This is in line with the concept that in repeated samples, the calculated confidence intervals would contain the true population mean a certain percentage of the time, indicating that a range of values around the sample mean are plausible estimates of the true mean.