The correct answer is $\boxed{\text{B) }0.034}$.
The probability of a Poisson distribution with mean $\mu$ of less than $k$ events is given by the following formula:
$$P(X < k) = \sum_{i=0}^{k-1} \frac{\mu^i e^{-\mu}}{i!}$$
In this case, $\mu = 5.2$ and $k = 2$. Substituting these values into the formula, we get:
$$P(X < 2) = \sum_{i=0}^{1} \frac{5.2^i e^{-5.2}}{i!} = 0.034$$
The other options are incorrect because they do not correspond to the correct probability.
Option A, $0.029$, is the probability of a Poisson distribution with mean $\mu = 5.2$ of exactly one event.
Option C, $0.039$, is the probability of a Poisson distribution with mean $\mu = 5.2$ of exactly two events.
Option D, $0.044$, is the probability of a Poisson distribution with mean $\mu = 5.2$ of three or more events.