A standard normal distribution has a mean of zero and standard deviation of 1. So, A is not true for all normal distributions.

A normal distribution is completely described by the mean and standard deviation (variance, naturally).

The without limit part is correct. Theoretically, the tails of the distribution extend indefinitely, and the probability under the curve gets infinitesimally small in these regions.

I don’t have any idea what I mean by nontheoretically. tickersu qualified his answer with “theoretically”, so I was just tryint to ascertain what happens without that qualification.

(Personally, I despise the adverb “theoretically”. Generally, the perpetrator of this word has no idea to what theory they’re referring, so the word is meaningless, and the conclusions even more so.)

what happens without that qualification is that you need another page (theoretically infinity pages ) to illustrate the normal distribution, ie. no text book has ever replicated it with accuracy

Well, based on the fact that you’re not going to observe these infinite tail limits in practice, it is more of a theoretical idea, isn’t it? My qualification was to point out that you’re not going observe these bounds in a practical scenario, but the bounds of this theoretical normal distribution are +/- infinity.

Also, feel free to correct my conclusion if it is meaningless/incorrect.

The mean can be any real number; the SD must be greater than 0. The variance can definitely be very large, but infinite? I would have to think on that one and maybe even dig out an old stats textbook.

For a standard distribution, with a given mean and standard deviation it means that the probablility that an observed value is +/- infininty is greater than zero.

For example, P(X>n) > 0 for any n in the set of real numbers.