Answer
(a) For an object to stay at rest, the coefficient of static friction $\mu_s$ must be at least $\frac{a}{g}$.
(b) The chair would have started to slide on the floor.
Work Step by Step
(a) $F_f = ma$
$mg ~\mu_s = ma$
$\mu_s = \frac{a}{g}$
For an object to stay at rest, the coefficient of static friction $\mu_s$ must be at least $\frac{a}{g}$.
(b) $\frac{a}{g} = \frac{4.0 ~m/s^2}{9.80 ~m/s^2} = 0.41$
Since $0.25 < 0.41$, the coefficient of static friction $\mu_s < \frac{a}{g}$. Therefore, the chair would have started to slide on the floor.