CLT: Normal(0.5*N*(a+b), 0.5*(b-a)*sqrt(N/3) ).

In your first example, N=1000, a=0.7, b=1.3

Then

Mean=0.5*1000*(0.7+1.3)=1000

sigma (i.e. Standard Deviation ) =
0.5*(1.3-0.7)*sqrt(1000/3)=5.477226
Variance=sigma^2=30

With those parameters, you can get any probability simply by Normal distribution table or function. Excel is good enough.

Why do you need simulation (particularly only 50 times)?