Are the eigenfunctions of H for the particle in the one-dimensional box also eigenfunctions of the position

Are the eigenfunctions of Hˆ for the particle in the one-dimensional box also eigenfunctions of the position operator x̂ ? Calculate the average value of x for the case where n = 3. Explain your result by comparing it with what you would expect for a classical particle. Repeat your calculation for n = 5 and, from these two results, suggest an expression valid for all values of n. How does your result compare with the prediction based on classical physics?