Each ball makes n independent left/right choices. The number of right-bounces is Binomial(n, p), which approaches a normal distribution as n grows (de Moivre–Laplace).
Orange curve: N·φ((k − np)/σ)/σ with σ² = np(1 − p), scaled to the number of balls landed. Bars are bin counts of k, the number of rightward bounces.