= Solution
For a thickness $x$ with <number density> $\rho_n$ of scattering centres, the mean count is $N=\rho_nx\sigma$. Using the total <cross section> in <4/b/i> and the <variance> addition in <4/b/ii>,
$$
\begin{aligned}
\operatorname{RMS}(\theta)^2
&\simeq\rho_nx\frac{16\pi K}{p^2\theta_{\min}^2}\,2\theta_{\min}^2\ell\\
&=\frac{32\pi K\rho_nx\ell}{p^2}.
\end{aligned}
$$
Thus
$$
\boxed{\operatorname{RMS}(\theta)\simeq\sqrt{32\pi K\rho_n\ln(\theta_{\max}/\theta_{\min})}\,\frac{\sqrt x}{p}.}
$$
The stated assumptions make the prefactor independent of $x$ and approximately independent of $p$. The lower-cutoff factors cancel except inside the slowly varying logarithm. Treating $N$ as a <Poisson random variable> rather than a fixed count gives the same result after replacing $N$ by its mean.
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