Calculate following probabilities area under the curve for t

Calculate following probabilities (area under the curve) for the standard normal variable, z:

a. P(– z 1.01) =

b. P(0 z 2.5) =

c. P(– z ) =

d. P(–1.25 z 3.19) =

e. P(– z –0.44) =

Solution

A) From the Normal table we have

P(– z 1.01) = P(– z < 0)+ P(0 < z 1.01)  

                              =0.5+0.3438                                      Normal table

                               =0.8438

B) P(0 z 2.5) =0.4938 from Normal table

C) P(– z ) =1           Total area is 1

D)

P(–1.25 z 3.19) =P(–1.25 z < 0)+P(0 < z 3.19)

                                   =P(0 < z 1.25) +P(0 < z 3.19)                  symmetric property of normal curve

                                   =0.3944+0.4993                                               Normal table

                                   =0.8937

E)

P(– z –0.44) =P(– z < 0) – P(–0.44 z <0)

                                =0.5 – P0 < z 0.44)                     symmetry of normal curve

                                =0.5 – 0.1700

                               =0.33