3 problems

Quantitative Erdős–Kac conjecture for irreducible quadratics. The Kolmogorov distance between $X_N$ and the standard Gaussian $\mathcal{N}(0,1)$ is…

Quantitative Erdős–Kac conjecture for Beatty sequences. The distance between $X_N$ and the standard Gaussian $\mathcal{N}(0,1)$ is bounded above by

Erdős–Kac conjecture for integer parts of polynomials. The random variable $X_N$ converges in distribution to the standard Gaussian $\mathcal{N}(0,1)$ as $N\rightarrow\infty$.