Probability of p(-4<X-u<4) from a list?

alright, bit of confusion, im given a decent sized list, but thanks to the TI83 ill just cut to the simple parts,

i get a Sx of 16.244, n=28, xbar of 76.96, sample variance of 263.8875, population standard deviation of 15.951

im asked what distribution would the mean of X bar follow (never could figure out which distribution i should use)

lastly im asked what is the probability of P(-4≤X-u≤4) (x=xbar and u=mew)

i guess where im really confused is the fact that its x- u, and not just a zscore or something

Thanks in advance for any help...ill find some part of this forum where i can be helpful to return the favor.