I am working on a model which predicts the total final score (sum of the scores of both teams) of certain sports matches. I have checked the predictions of the model against the actual scores of matches for the last several years. The error in the predicted total score to the actual toal score is approximately normally distributed with mean $=-0.3$ and standard deviation $= 13$.
Say I have a predicted total score $x$, how can I determine the probability that the actual score will above or below a given score line $y$.
For example, say my model predicts that the total score will be $8$ and the score line is $5.5$, what is the probability that the actual score will be $\le 5$ and what is the probability that the actual score will be $>5$ (given that the errors in my prediction can be assumed to be normally distributed)?