The distribution of genera of 2-bridge knots

The average genus of a 2-bridge knot with crossing number $c$ approaches ${c}/{4} + {1}/{12}$ as $c$ approaches infinity, as proven by Suzuki and Tran and independently by Cohen and Lowrance. In this paper, for the genera of $2$-bridge knots of a fixed crossing number $c$, we show that the median and mode are both $\lfloor \frac{c+2}{4} \rfloor $ and that the variance approaches ${c}/{16}-{17}/{144}$ as $c$ approaches infinity. We prove that the distribution of genera of 2-bridge knots is asymptotically normal.