The sum of uniforms is not a uniform so I had expected a central limit problem here.
But with n=12 that's not really appropriate.
you can multiply by 12 and then figure out
which is a 12 fold integral with density 1.
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!!