Getting a new distribution for X(bar)

Let X(bar) be the mean of a random sample of size 12 from the uniform distribution on the interval (0,1).

Approximate P(1/2 < X(bar) < 2/3).

No idea how to do this whatsoever.

I know you can use the moment generating function but I can't simplify it to make it work.

And sorry I can't overscore? on here, so X(bar) is sample mean.

Also, a general idea of how to approach these problems would be helpful too, I have other similar practice problems.

Any help would be greatly appreciated.

Thanks in advance!!