SAT Question 0108ac2d: Inference From Sample Statistics And Margin Of Error answer and explanation with Desmos solution

Choice C is correct. It's given that an estimated $38\%$ of sampled students at the school were in support of a menu change, with a margin of error of $5.5\%$. It follows that the percent of the students at the school who support a menu change is $38\%$ plus or minus $5.5\%$. The lower bound of this estimation is $38-5.5$, or $32.5\%$. The upper bound of this estimation is $38+5.5$, or $43.5\%$. Therefore, plausible values of the percent of the students at the school who support a menu change are between $32.5\%$ and $43.5\%$.