$F_b = 16.5 ~ \text{MPa}$
$F_v = 1.73 ~ \text{MPa}$
$E = 7.31 ~ \text{GPa}$
Part 1: Maximum flexural stress
$M = \dfrac{w_o L^2}{8}$
$M = \dfrac{10(4^2)}{8}$
$M = 20 ~ \text{kN}\cdot\text{m}$
$f_b = \dfrac{6M}{bd^2}$
$f_b = \dfrac{6(20)(1000^2)}{190(250^2)}$
$f_b = 10.105 ~ \text{MPa}$ answer
$f_b \lt F_b$ (okay)
Part 2: Maximum flexural stress
$V = 20 ~ \text{kN}$
$f_v = \dfrac{3V}{2bd}$
$f_v = \dfrac{3(20)(1000)}{2(190)(250)}$
$f_v = 0.6316 ~ \text{MPa}$ answer
$f_v \lt F_v$ (okay)
Part 3: Maximum deflection
$I = \dfrac{bd^3}{12}$
$I = \dfrac{190(250^3)}{12}$
$I = 247\,395\,833 ~ \text{mm}^4$
$\delta = \dfrac{5w_o L^4}{384EI}$
$\delta = \dfrac{5(10)(4)(1000^4)}{384(7\,310)(247\,395\,833)}$
$\delta = 18.43 ~ \text{mm}$ answer
