How do I find the Z score for a statistic without standard deviation given Pop mean=.05%, n=100, Sample mean of .11%?
By definition, Z score is:
Unless I misunderstood your problem, I see no way you can calculate this number without knowing a standard deviation.
I think the problem is really about a proportion so you do not need the standard deviation to find the standardized test statistic z. See the Explanation for the formula.
In your question, the sample proportion (p-hat) is 0.11%. The population proportion, p, is 0.05%. Use the following procedure: