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"It has long been an axiom of mine that the little things are infinitely the most important" 

Just a note
For a sample as small as this, central limit theorem is not likely to be very effective. The dashed line indicates the fitted normal distribution. From this very limited information we have no reason to suppose their mean would be nonnormally distributed.
However, in fitting a confidence interval to this mean we are also assuming these observations are a random sample  which is not quite so easy to check...
