A sphere can roll on a surface inclined at an angle θ provided that...

When the sphere is released on the inclined plane, the component of gravity along the incline is $mg\sin\theta$, which tends to slide the sphere downwards.

Since the coefficient of friction is non-zero (given as $\mu = \dfrac{1}{7}g\tan\theta$ or assuming a typo for $\dfrac{1}{7}\tan\theta$), a frictional force will act on the sphere at the point of contact in the upward direction along the incline.

This frictional force provides a torque about the centre of mass of the sphere ($\tau = f \times R$), which produces an angular acceleration. Thus, the sphere will rotate about its centre.

The required friction for pure rolling is $f = \dfrac{2}{7}mg\sin\theta$. Even if the available friction is less than this value, kinetic friction will act, which is still greater than zero. The net force along the incline is $F_{net} = mg\sin\theta - f$. Since $f$ is either $\dfrac{2}{7}mg\sin\theta$ (for pure rolling) or $\mu mg\cos\theta$ (for slipping), $F_{net}$ is always positive.

Thus, the sphere will have both translational motion down the incline and rotational motion about its centre.