I'm currently researching the variability of sizes of potatoes when all of the potatoes in question have been harvested from a single field. One question keeps coming up in my statistical analyses: Under normal circumstances, are the sizes of potatoes - within a single field - normally distributed? (Please feel free to define the weasel words "normal circumstances" in the most helpful way you can imagine.)
Human height is often given as one of those classic examples of a normally distributed phenomenon. The little that I know about plant biology suggests that the central limit theorem applies just as much to potatoes as to the human body: the lengths of potato tubers and the lengths of human bones should have similarly-shaped distributions. But is that correct?
A bit of context to my original question: what I'm trying to do is to take the mean and standard deviation of my data and then, using the 68-95-99 rule, construct a series of confidence intervals, which I can then test or refine by looking at other data sets. Obviously, no real data set is going to conform perfectly to a model; I just need to know that, in principle, potato sizes are normally distributed enough that my method for drawing up confidence intervals isn't hopelessly misguided.