2005 AMC 12B Problem 9

The percentage scoring $95$ is $100 - 10 - 25 - 20 - 15 = 30.$ The mean is $$\begin{aligned} &0.10(70) + 0.25(80) \\ &\quad {}+ 0.20(85) + 0.15(90) \\ &\quad {}+ 0.30(95) = 86. \end{aligned}$$ Cumulatively, $10\%$ are below $80,$ $35\%$ are at or below $80,$ and $55\%$ are at or below $85.$ The middle scores fall at $85,$ so the median is $85.$ The difference is $86 - 85 = 1.$ Thus, the correct answer is B.