Solution
= Solution
Since $q$ is an <even function>, $tq(t)$ is an <odd function> and its <integral> over the symmetric interval vanishes. Thus $\mathbb E[T]=0$. Its <variance> is
$$
\mathbb E[T^2]=2\int_0^1t^2(1-t)\,dt
=2\left(\frac13-\frac14\right)=\frac16.
$$
Consequently
$$
\boxed{\mathbb E[T]=0,\qquad\operatorname{SD}(T)=\frac1{\sqrt6}\text{ minute}}.
$$
The <standard deviation> is approximately $0.40825$ minute, or $24.49$ seconds.