You want to calculate the standard deviation of your set of data.
This type of probability is called single variable statistics.
I have attached an excel file that will help you get started.
I would say that this is not a normal distribution and that there are significant differances in the neighborhoods. Mainly because some of the neighborhoods fall much more than one standard deviation away from the mean (average).
Also just by looking at the frequency graph this does not look like a normal curve.
Hopefully someone can follow up and help some more.