Probability Question

Haven't really pencil down anything, but what you're supposed to find is this:

$X_{n}$: RV of the number of shots in the nth session, so $X_{n} \sim NB(8, 0.3)$, and
$T_{25} = \sum^{25}_{i=1}X_{i}/25$, with each $X_{i}$ being iid (independent and identically distributed).
Our goal is to find $P(T_{25}<25)$.
(P.S. I put subscripts here, because you can generalize this)

So some sessions could take more than 25 shots, but on the whole you need less than 25 on average.
This is hard to find (maybe it's easy, but I'm too sleepy to figure it out...).

But rephrase this question a bit, this is essentially asking for "less than 25 attempts on average in 25 sessions with 8 successes each session", which is the same as "less than 25*25 attempts with 8*25 successes in total" (why?). The latter is easier to manage. Granted I think you still need the CMF of negative binomial...