Apopulation has a mean of μ = 80 and a standard deviation of σ = 20. would a score of x = 70 be considered an extreme value (out in the tail) in this sample? if the standard deviation were σ = 5, would a score of x = 70 be considered an extreme value?

Using the z-score, it is found that:

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In this distribution:

The z-score is:

With a standard deviation of

A similar problem is given at link

With a sigma of 20, a score of 70 is half a standard deviation below the mean 80,  z=-1/2.    I don't know if there's an official definition, but I consider values extreme if the absolute values their z scores is say 3 or more.  So no, this is not extreme at all.

If the standard deviation is 5 instead of 20, then 70 is 2 standard deviations below the mean (z = -2).  I still wouldn't consider that an extreme value.