Answer :
The variance is given by:
[tex]\sigma^2=\frac{\Sigma(x-\mu)^2}{N}[/tex]Therefore:
[tex]\begin{gathered} \mu=\frac{5\cdot0.1+6\cdot0.1+7\cdot0.3+8\cdot0.1+9\cdot0.4}{5} \\ \mu=1.52 \end{gathered}[/tex][tex]\begin{gathered} \sigma^2=\frac{160.152}{5} \\ \sigma^2\approx32.0 \end{gathered}[/tex]