This seems like it should be easier than it is, but I'm stuck trying to determine if a data set I have represents a truncated normal distribution. The hypothesis I'm testing is that the data you see below is actually acting as a truncated normal distribution rather than a Poisson or geometric distribution. By being able to calculate the parent mean and standard deviation from the truncated set, I could then go on to extrapolate how the given data set would react without the limitation at the truncation.
I'm trying to avoid an iterative process, but can write that code and deal with the resources if absolutely necessary. How can I determine the parent mean and standard deviation from this truncated data set?
Please bear in mind my background is in business and finance rather than statistics, so I apologize in advance for any misuse of terms or elementary basis of understanding on some of the higher statistical concepts.