An article in International Journal of Electrical Power & Energy Systems [“Stochastic Optimal Load Flow Using a Combined Quasi–Newton and Conjugate Gradient Technique” (1989, Vol.11(2), pp. 85–93)] considered the problem of optimal power flow in electric power systems and included the effects of uncertain variables in the problem formulation. The method treats the system power demand as a normal random variable with 0 mean and unit variance.

(a) What is the power demand value exceeded with 95% probability?

(b) What is the probability that the power demand is positive?

(c) What is the probability that the power demand is more than – 1 and less than 1?