Answer
18 seconds.
Work Step by Step
$P(x)=\frac{(λt)}{x!}e^{-λt}$
$λ=10$ and $t=?$
$P(0)=\frac{(10t)^0}{0!}e^{-10t}=e^{-10t}$
We want:
$P(X\geq1)=0.95$
$1-P(0)=0.95$
$P(0)=0.05$
$e^{-10t}=0.05$
$-10t=\ln{0.05}$
$t=\frac{\ln{0.05}}{-10}\approx0.30~min=18~s$
