Final answer:
Based on the given options and typical margins of error for confidence intervals, option c (39.5, 44.5) appears to be a reasonable range for the 95 percent confidence interval for the percentage of Americans who approve of President Biden's handling of the economy. Without the exact standard error or margin of error, we cannot confirm the precise interval boundaries.
Step-by-step explanation:
The recent YouGov poll indicates that 42.0 percent of Americans approve of President Biden's handling of the economy. This approval is within a confidence interval, which, if we are 95 percent confident, sets a range of values (x percent to y percent) where the actual approval percentage is likely to lie. To determine the correct range, we look at the offered options and apply the concept of confidence intervals in statistics.
Generally, when a confidence interval is constructed for a population proportion based on sample statistics, we use the standard error of the proportion and a critical value (z-score) corresponding to the desired level of confidence. However, without the actual standard error or margin of error provided, we cannot perform the precise calculation needed to determine the exact confidence interval bounds. Instead, we will have to match the reported confidence interval with the given options based on typical confidence interval ranges.
Based on common confidence interval calculations for proportions, option c (39.5, 44.5) seems reasonable as a typical margin of error would likely produce a range of approximately 3 percentage points above and below the reported sample proportion. The exact numbers, however, would depend on the specific margin of error, which is not provided in the question.