z0 z1 z128 z1645 z196 z233 PZ

z=0

z=1

z=1.28

z=1.645

z=1.96

z=2.33

P(Z<=0)=0.5

P(Z<=1)=0.84

P(Z<=1.28)=0.9

P(Z<=1.645)=0.95

P(Z<=1.96)=0.975

P(Z<=2.33)=0.99

Given above table, the probability P(- 1 <= Z <= 1) is

Solution

P(- 1 <= Z <= 1) = P(Z <= 1) - P(Z <= -1)

                        =P(Z <= 1) - P(Z >= 1)

                        = P(Z <= 1) -[1- P(Z <= 1)]

                         = 2*P(Z <= 1) -1

                         =2*0.84 -1   =0.68