Butterfly-style valves used in heating and ventilating industries have a high flow coefficient. Flow coefficient can be modeled by a normal distribution with mean \(496 C_{V}\) and standard deviation \(25 C_{v}\). Find the probability that a valve will have a flow coefficient of

(a) at least \(450 \mathrm{C}_{\mathrm{v}}\);

(b) between 445.5 and \(522 \mathrm{C}_{\mathrm{V}}\).