Question

Find the following z values for the standard normal variable Z. (You may find it useful to reference the z table. Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)

a. P(Z ≤ z) = 0.1065

b. P(z ≤ Z ≤ 0) = 0.1746

c. P(Z > z ) = 0.9412

d. P(0.4 ≤ Z ≤ z) = 0.3177

Answer 1

a.

P(Z z ) = 0.1065

From standard normal tables , z = -1.245

P(Z<-1.24) = 0.1075 and P(Z<-1.25) = 0.1056

so approximately z = - 1.245

b.

From standard normal tables

P(Z0) = 0.5

From standard normal tables, P(Z-0.45) = 0.3264

so approximately z = - 0.45

c. P(Z > z ) = 0.9412

P(Z > z) = 1-P(Zz) = 0.9412

P(Zz) = 1-0.9412 = 0.0588

From standard normal tables

P(Z-1.56) = 0.0594

P(Z-1.57) = 0.0582

so approximately z = - 1.565

d. P(0.4Zz) = 0.3177

P(0.4Zz) = P(Zz) - P(Z0.4) = 0.3177

From standard normal tables ,

P(Z0.4) = 0.6554

P(Zz) = 0.3177+0.6554 = 0.9731

From standard normal tables ,

P(Z1.93) = 0.9732

so approximately z = 1.93