From the z-table:

(a)This is the same as asking "What is the area to the right of `1.06` under the standard normal curve?"

We need to take the whole of the right hand side (area `0.5`) and subtract the area from `z = 0` to `z = 1.06`, which we get from the z-table.

`P(Z >1.06)` `=0.5-P(0< Z<1.06)` `=0.5-0.355` `=0.1446`


(b)This is the same as asking "What is the area to the left of `-2.15` under the standard normal curve?"

This time, we need to take the area of the whole left side (`0.5`) and subtract the area from `z = 0` to `z = 2.15` (which is actually on the right side, but the z-table is assuming it is the right hand side.)

`P(Z <-2.15)` `=0.5-P(0< Z <2.15)` `=0.5-0.4842` `=0.0158`


(c) This is the same as asking "What is the area between `z=1.06` and `z=4.00` under the standard normal curve?"

`P(1.06< Z <4.00)`

`=P(0< Z <4.00)-` `P(0< Z <1.06)`

`=0.5-0.3554`

`=0.1446`


(d) This is the same as asking "What is the area between `z=-1.06` and `z=4.00` under the standard normal curve?"

We find the area on the left side from `z = -1.06` to `z = 0` (which is the same as the area from `z = 0` to `z = 1.06`), then add the area between `z = 0` to `z = 4.00` (on the right side):

`P(-1.06< Z <4.00)`

`=P(0< Z <1.06)+` `P(0< Z <4.00)`

`=0.3554+0.5`

`=0.8554`

Easy to understand math videos:
MathTutorDVD.com