The area under the entire normal curve is 1. So the area under each side
of the normal curve is .5. We want to find the value of z such that 70% or .70
of the area is under the curve to the right of that
So .50 of the .70 is to the right of z=0 and that leaves
.70 - .50 = .20 for the area on the left of z=0.
So we look in the body of the normal table and find the nearest value to
.20 for the area to the left of z=0 that we need to make up the rest of the
70%. We find that .1985 is the closest area value in the table. Then we
observe that .1985 occurs where z = -0.52. We know to take it negative since
only negative values of z have more than 60% of the area to the right of them.
So that is the value we are looking for. I'll indicate it with a green line
at z=-0.52, just a little past halfway between z=0 and z=-1.
The area under the curve to the right of the green line at z=-0.52 is 70%
of the entire area