The mean of the standard normal curve is at z=0.
You want the value of z such that the area under the curve
between it and z=0 is .40.  That is, the shaded region below
is to be .40

 

To find that value look in the body, not the z values,
but the 4-place decimal values of your table until you find the 
closest value to .4000.  You find the values .3997 which is the nearest
value under .4000, and .4015 which is the nearest above .4000. The closer 
of these to .4000 is .3997, and the leftmost column on that row is 1.2 and 
the heading of the column it is in is 0.08, so the value in 1.28.  However,
the shaded area is on the left which is the negative side, so the answer is
-1.28.

You can also find it on your TI-84 calculator, but on the calculator
you have to find the z-value that has the other 10% (50%-40%) to the
left of it:

 

Press ON
Prss CLEAR
Press 2ND
Press VARS
Press 3

you should see invNorm(

after that type .1) 

you should see  invNorm(.1)

Press ENTER

Read -1.281551567

Round that to -1.28.

Edwin