Step 1. First important thing to realize is that the force exerted on the floor by the ball is a reaction force to the normal force $F_N$ . Due to Newton's third law (actually, as a consequence of conservation of momentum), the magnitude of this force is the same as $F_N$ of the floor on the ball so let's find that!

Step 2. The normal force can be found using Newton's second law from a free body diagram: $F_{net}=F_N-F_g$

Step 3. Newton's second law also states that $F_{net}=\frac{\text{∆p}}{∆t}$ which we can use to find a value for $F_{net}$ .

Step 4. Read some information from the graph:

∆t = 0.1 s (the time of impact with with floor)

$v_1=-10\frac{m}{s}$ (velocity right before reaching the floor)

$v_2=+5\ \frac{m}{s}$ (velocity fright after bouncing back up from the floor)

Step 5. Find the net force

$F_{net}=\frac{m_{ }\times v_2-m\times v_1}{∆t}$

$F_{net}\ =\ \frac{0.25\ \left(5-\left(-10\right)\right)}{0.1}=37.5\ N$

Step 6. Use it to solve for $F_N$ :

$F_N=F_{net}+F_g$

$F_N=F_{net}+mg$

$F_N=\ 37.5\ N\ +\ 0.250\ \times9.80\ N$

$F_N=40\ N$