Ineed with this problem. find the standard score (z) such that the area above the mean and below z is about 34% of the area under the normal curve.

For the normal distribution:
one standard deviation from the mean accounts for about 68.2% of the set

two standard deviations from the mean account for about 95.4%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve:
Below: z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and 50% to the right