Normal densityContinuous Random Variables Please show all de

(Normal density-Continuous Random Variables)     Please show all details so I may learn the process. Thank you.

Solution

Given that µ = 3 and ² = 9 that implies = 3

According to area property of normal probability integral we have

P(X-3>6) = P(X-3<=6)

                      = P(-3<X<9)

                     = P(-2<Z<2)

                    = 2*P(0<=Z<=2)

                   = 2*0.4772

                    = 0.9544

P(X-3>6) =1- P(X-3<=6)

                     = 1 – 0.9844

                      = 0.0456

Working : Z = (X- µ)/

            Z= (-3-3)/3 = (-6)/3 = -2

            Z = (9-3)/3 = (6)/3 = 2