GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

The sum of two Normally distributed functions is always normally distributed.
$\mathit{X}={\mathit{f}}_{\mathit{N}}\left(\mathit{\mu }\mathit{x},{\mathit{\sigma }}_{\mathit{x}}^2\right)$
$\mathit{Y}={\mathit{f}}_{\mathit{N}}\left({\mathit{\mu }}_{\mathit{Y}},{\mathit{\sigma }}_{\mathit{y}}^2\right)$
Where subscript $\mathit{N}$ stands for normally distribution
$\mathit{M}\mathit{x},{\mathit{\mu }}_{\mathit{y}}$ are means and ${\mathit{\sigma }}_{\mathit{x}}^2,{\mathit{\sigma }}_{\mathit{y}}^2$ are variances of function $\mathit{X}$ and $\mathit{Y}$ respectively.
$\mathit{Z}=\mathit{X}+\mathit{Y}={\mathit{f}}_{\mathit{N}}\left({\mathit{\mu }}_{\mathit{X}}+{\mathit{\mu }}_{\mathit{Y}},{\mathit{\sigma }}_{\mathit{x}}^2+{\mathit{\sigma }}_{\mathit{y}}^2\right)$