22400 cc of N₂ at STP contain N_A molecules, the number of molecules present at 1 cc of N₂ at STP contains:

$\begin{array}{ccc}1 \mathrm{cc} {\mathrm{N}}_2 \mathrm{molecules}& =& 1\mathrm{cc}\times \frac{6.022\times {10}^{23} \mathrm{molecules}}{22400 \mathrm{cc}}\\ & =& 2.69\times {10}^{19} \mathrm{molecules}\end{array}$

Statement I is correct.

One mol of any gas at STP occupies 22.4 L and the number of moles of gas at STP condition is equal to the Avogadro's number, $6.022\times {10}^{23} \mathrm{molecules}.$

Statement II is correct.