The final volume of the solution is of no importance for determining the mole fraction of sodium iodide in the solution, so you can ignore it altogether.
You can think of the mole fraction of sodium iodide in the solution as the ratio between the moles of sodium iodide and the total number of moles the solution contains, i.e. moles of solute and moles of solvent.
Use sodium iodide and water's molar masses to determine how many moles of each you have
This means that the total number of moles present in the solution will be
Therefore, the mole fraction of sodium iodide will be