Probability & Central Limit Theorem

This is what I have so far.
σx = σ/ √n = 1.2/ √35 = 0.2028

z = x̄ - μx̄/σx = x̄ - μx̄/σ/√n = 12,749 - 12,752/ 1.2√35 = -0.4226 = .33724

I stopped right there because I got confused. I'm stuck.

If I understand your problem correctly, you have your formula slightly wrong.

z = (x̄ - μx̄)/σx =( x̄ - μx̄)/(σ/√n) = (12,749 - 12,752)/ (1.2√35) = -14.8

If you look up this z score in a table or just use an internet calculator, you see that the chance of being fourteen standard deviations from the mean is zero. Since that is a really unusual answer, it makes me wonder if I read it correctly.