This seems like such a simple question, and I should know it, but for some reason I cannot figure it out and cannot find an answer via googling

I have a guassian distribution for the average number of days a snake sits idle in its burrow before leaving to find food. Let's say the mean is 5 and the standard deviation is 2. Let's further assume that a 'leaving' event is independent from other leaving events (if it leaves one day to find food, regardless of what happens, it will have the same probability to leave to find food the next day).

How can I find the probability that a snake will leave its burrow each day?

I know this is some sort of Binomial or Bernoulli distribution, but when I try reading about this things to find help, the explainations do not describe how to derive the p parameter; or if they do its just beyond my ken.