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What is non normal distribution?
A distribution that is NOT normal. Most of the time, it refers to skewed distributions.
Is a normal distribution extremely skewed or oddly shaped?
It is not at all skewed. As to oddly shaped, it depends on your expectations.
When population distribution is right skewed is the sampling also with right skewed distribution?
If the population distribution is roughly normal, the sampling distribution should also show a roughly normal distribution regardless of whether it is a large or small sample size. If a population distribution shows skew (in this case skewed right), the Central Limit Theorem states that if the sample size is large enough, the sampling distribution should show little skew and should be roughly normal. However, if the sampling distribution is too small, the sampling distribution will likely also show skew and will not be normal. Although it is difficult to say for sure "how big must a sample size be to eliminate any population skew", the 15/40 rule gives a good idea of whether a sample size is big enough. If the population is skewed and you have fewer that 15 samples, you will likely also have a skewed sampling distribution. If the population is skewed and you have more that 40 samples, your sampling distribution will likely be roughly normal.
Who invented skewed distribution?
Nobody invented skewed distributions! There are more distributions that are skewed than are symmetrical, and they were discovered as various distribution functions were discovered.
Why does a binomial distribution become more skewed as n increases?
As n increases, the distribution becomes more normal per the central limit theorem.
