What is the z value such that 52% of the data are to its left?
The answer is z = 0.05 in a normal distribution.
To solve this problem, you will need access to a z-table (also called a "standard normal table") for the normal distribution. There is a good one on Wikipedia.
By asking what is the value of z such that 52% of the data are to its left, your goal is to find a z-value where the cumulative area up to the value of z sums to 0.52. Therefore you need a cumulative z-table.
Find the entry in the cumulative z-table that shows where a certain value of z is closest to an output in the table of 0.52 (which is 52% of of the cumulative distribution). In this case, the z value of 0.05 results in the closest value to 0.52.