Answer
$$494 \mathrm{\ m} / \mathrm{s}$$
Work Step by Step
We can express the ideal gas law in terms of density using $n=M_{\text {samp }} / M:$
$$p V=\frac{M_{\text {sum }} R T}{M} \Rightarrow \rho=\frac{p M}{R T}$$
We can also use this to write the rms speed formula in terms of density:
$$v_{\text {ms }}=\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3(p M / \rho)}{M}}=\sqrt{\frac{3 p}{\rho}}$$
We convert to SI units: $\rho=1.24 \times 10^{-2} \mathrm{kg} / \mathrm{m}^{3}$ and $p=1.01 \times 10^{3} \mathrm{Pa}$.
Then the rms speed is
$$\sqrt{3(1010) / 0.0124}=494 \mathrm{m} / \mathrm{s}$$
