Let X N1052 Answer the following questions about X I would

Let X ~ N(10,52). Answer the following questions about X, I would suggest computing these using the normal table provided on Learn (you will not have R on the exams!), but you can check your answers using R if you wish. Find P(X 11). Find P(X 8.4). Find x such that P(X x) = 0.95.

Solution

a) P(X < 11) = P(Z < (11 - 10)/5 )

                    = P(Z < 0.2)

                    = 0.5793

b) P(X > 8.4) = P(Z > (8.4 - 10)/5 )

                    = P(Z > -0.32)

                   = 1 - P(Z < -0.32)

                   = 1 - 0.3745 = 0.6255

c) P(X < x) = 0.95

or, P(Z < (x - 10)/5 ) = 0.95

or, (x - 10)/5 = 1.65

or, x = 18.25