SAT Question fc46af57: Inference From Sample Statistics And Margin Of Error answer and explanation with Desmos solution

Choice B is correct. It was estimated that $15\%$ of the beads in the bag are red. Since the bag contains $10,000$ beads, it follows that there are an estimated $10,000\times 0.15=1,500$ red beads. It's given that the margin of error is $2\%$, or $10,000\times 0.02=200$ beads. If the estimate is too high, there could plausibly be $1,500-200=1,300$ red beads. If the estimate is too low, there could plausibly be $1,500+200=1,700$ red beads. Therefore, the most plausible statement of the actual number of red beads in the bag is $1,300<r<1,700$.