You must define your distribution. Are you trying to do something else first?
We have 0.04 breakdowns per week. What kind of a distribution might that suggest? It breaks down or it doesn't...Sounds sort of Bernoulli, doesn't it? p = 0.04 (Break down) and q = 0.96 (Survive)
If we notice that we have 38 machines, it may sound as if we are running the same Bernoulli experiment 38 times.
This should sound rather Binomial, with p = 0.04, n = 38, and E[x] = 38*0.04, Var(x) = 38*0.04*0.96.
What do you think about Poisson with ?
Well, maybe again, but we've only 38 machines. I suppose they could break down more than once, each, but I think I'm stretching it,
Once you've pinned down the distribution, the rest can be cake. What say you?