It appears to me (assuming I'm reading your question right) that this is just an application of the central limit theorem (CLT). Basically the mean of any distribution follows a standard normal distribution if you standardize it (subtract the true mean and divide by the std) so that is the distribution you need to use.. the nice thing here is that they have already subtracted the mean for you so you don't have to do that... all you have to do is divide all three sides of the inequality by the standard deviation and use a standard normal table to obtain the probability.
It would look like this...
P(-4 < xbar - mu < 4) = P(-4/3.01 < (xbar - mu)/sigma/Sqrt(n) < 4/3.01)
= P(-1.33 < Z < 1.33)
= Phi(1.33) - Phi(-1.33) = 0.815
(Look up Z of 1.33 in a normal table or use computer software to find the probability)
Hope that helps!