How should I implement the state transition when it is a Gaussian distribution?

Question

I am reading this paper Anxiety, Avoidance and Sequential Evaluation and is confused about the implementation of a specific lab study. Namely, the authors model what is called the Balloon task using a simple MDP for which the description is below:

My confusion is the following sentence:

...The probability of this bad transition was modeled using normal density function, with parameters $N(16, 0.5)$

But the fact that this is a continuous, normal distribution makes me stumped. In MDP's, usually there is a nice, discrete transition matrix and so there is no ambiguity as to how to implement it. For instance, if they said the transition to a bad state is modeled by a Bernoulli random variable with parameter $p,$ then it is clear how to implement it. I would do something like:

def step(curr_state, curr_action):
   if uniform random variable(0,1) < p:
      next_state = bad state

But they are using a normal random variable for this "bad" transition, so how do I implement this?

Answer 1

I figured this out by going to the author's publicly available github code. It turned out the authors were just generating the transition probability $p$ from $\mathcal{N}(\mu,\sigma^2)$ at the beginning of each episode for some reason. Answering it myself for the sake of not leaving this question unanswered.