different between inherently vs normally

English

inherent +? -ly

inherently (comparative more inherently, superlative most inherently)

In an inherent way; naturally, innately.
Synonyms: see Thesaurus:intrinsically
- 1791, Thomas Paine, The Rights Of Man
  Rights are inherently in all the inhabitants; but charters, by annulling those rights, in the majority, leave the right, by exclusion, in the hands of a few.

normal +? -ly

normally (comparative more normally, superlative most normally)

Under normal conditions or circumstances; usually; most of the time
Normally, I eat breakfast at 6am, but today, I got up late and didn't eat until 9.
In the expected or customary manner.
Lisa ate normally, until she realised that she was late for choir, when she sped up.
To a usual or customary extent or degree.
He was abnormally agitated, she only normally so.
- 1984, Robert Charles Sproul, John Henry Gerstner, Arthur Lindsley, Classical Apologetics (?ISBN), page 178:
  An even more important reason is that our generation is not only normally ignorant but abnormally so. That is, we not only have scholars who do not know the history of the church's testimony, but we have those who tell it like it was not.
(mathematics, statistics) In the manner of a variable with a Gaussian distribution.

(most of the time): commonly, frequently, ordinarily; see also Thesaurus:usually
(in the expected manner): customarily, habitually, routinely; see also Thesaurus:normally
(to a usual degree): averagely
(mathematics):

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