How do I calculate the probability of a normally distributed random variable?

Take each one separately. P(X>1) U P(X<-3)

You have a N(-2, 1) random variable. First you'll need to standardize it so you can look up probabilities on a table.

To standardize any random variable, subtract the mean from the value you're comparing it too and then divide by the standard deviation.

So, for P(X>1) we'll go like this: (1-(-2))/1 = 3. That's your z statistic for the probability that the random variable is greater than 1. Make sure you get your probability for the area to the 'right' of 3 on the table, not the left of 3. (hint, it should be a very small value like 0.001 or something)

Do the same for P(X<-3): (-3-(-2))/1 = -1. That's your z stat. Get the area under the z curve to the left of -1 and that's your probability. Add what you got for the first one to this one.

I think you can take it from there. Contact me with any problems.