1 SD below accounts for 34% (one half 68) and 2 above account for 34+13.5=47.5%

That is because 95-68=27. 27/2=13.5

You can see from the graph of the normal distribution.

Add them up. one below to two above would be 34+34+13.5=81.5

From the tables, look up z=-1 and z=2. You should get close to 81.5

z=-1 corresponds to .1587. Then, .5-.1587=.3413

z=2 corresponds to .9772. Then, .9772-.5=.4772

.4772+.3413=.8185.

See?. Close to the graph method.