For this question, we don’t even need the value of $\lambda$ to get the answer.
It is good to remember this integration for solving questions on exponential distribution quickly.
$\int_{0}^{a} \lambda e^{-\lambda x} = 1 - e^{-\lambda a}$
So, with this,
$P (X \leq a) = 1 - e^{-\lambda a}$,
$P(X > a) = 1 – P(X \leq a) = e^{-\lambda a}$
$P (a \leq X \leq b) = P(X \leq b) – P(X \leq a) = (1 - e^{-\lambda b}) – (1 - e^{-\lambda a}) = e^{-\lambda a} – e^{-\lambda b}$
So, for this question the answer will be $P(X > E(X)) = P(X > \frac{1}{\lambda})$, which will be $e^{-\lambda *\frac{1}{\lambda}} = e^{-1} = 0.37$
Since the answer does not depend upon the value of $\lambda$, it means that it holds true for any exponential distribution.