We can find the variance of a binomial experiment as
[tex]\sigma^2=npq[/tex]
Using the relation
[tex]p+q=1\Rightarrow q=1-p[/tex]
Therefore the variance is
[tex]\sigma^2=np(1-p)[/tex]
We have the values of n and p, then
[tex]\begin{gathered} \sigma^2=np(1-p) \\ \sigma^2=10\cdot0.3\cdot(1-0.3) \\ \sigma^2=10\cdot0.3\cdot0.7 \\ \sigma^2=2.1 \end{gathered}[/tex]
And we know that the standard deviation is
[tex]\begin{gathered} \sigma^{}=\sqrt[]{np(1-p)} \\ \sigma^{}=\sqrt[]{2.1} \\ \sigma^{}=1.449 \end{gathered}[/tex]
Therefore the final answer is
[tex]\begin{gathered} \sigma^2=2.1 \\ \\ \sigma^{}=1.449 \end{gathered}[/tex]
