Formula for the probability that an RV is greater than b, if it’s normally distributed with mean μ and variance (σ^2):

P=1/Sqrt[2Pi  (σ^2)]Integrate[Exp[-(x-μ)^2/(2 (σ^2))],{x,b,Infinity}]

For example, the probability that an RV is greater than 0, if it’s normally distributed with mean 1/2 and variance 1/4:

P=1/Sqrt[2Pi (1/4)]Integrate[Exp[-(x-1/2)^2/(2*1/4)],{x,0,Infinity}]

N[P]