Answer
The normal force exerted by the floor on the chest is $750~N$
The frictional force on the chest due to the floor is $110~N$.
Since the force of static friction provides an equal and opposite force to the applied horizontal force, we don't need to know the coefficient of static friction to answer this question.
Work Step by Step
The normal force exerted by the floor on the chest is equal in magnitude to the chest's weight which is $750~N$
The frictional force on the chest due to the floor is equal in magnitude to the horizontal force of $110~N$.
Since the force of static friction provides an equal and opposite force to the applied horizontal force, we don't need to calculate the maximum possible force of static friction, which would be $F_N~\mu_s$. Therefore, it is not necessary to know the coefficient of static friction.
