If you just want to make a prediction about the proportion of nurses (and not do a z-test), you'll have to find more data points. You could sample several different employers, or look at different departments within the place where you work. In either case, you'd have many different proportions in your sample. You would calculate an average and standard deviation, and use that to estimate the population proportion (via a confidence interval).
Here is the statistics I have:
Hospital population is 5000 employees
Nurses employed at hospital is 1800
Different proportions in my sample: Nurses employed in intensive care units. 30 50 44 34 75 65 55 88
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Hospital population = 5000
Population of nurses = 1800
Proportion of nurses =p= 1800/5000=0.36
Calculate the standard ...
The solution examines population proportion statistics.