What is the difference between normal distribution and approximate normally. Correct me if im wrong but I think the parameters of Normal is X~Normal (mu, standard deviation) but then approx. normal is X~Normal (mu, variation) im just really confused when you use each and such.
Yes, you are correct. Read about the Central Limit Theorem. It might help to clarify the concepts for you.
You are partially correct in your understanding of the normal distribution and the concept of approximate normality. Let me clarify the terms and their usage.
The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is defined by two parameters: the mean (mu) and the standard deviation (sigma). It is denoted as X ~ N(mu, sigma).
The mean (mu) represents the central tendency or average value of the distribution, while the standard deviation (sigma) represents the dispersion or spread of the values around the mean. In a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.
Now, approximate normality refers to situations where a distribution is not precisely normal but can be approximated by a normal distribution. It commonly arises from the central limit theorem (CLT), which states that the sum or average of a large number of independent random variables tends to follow a normal distribution, regardless of the original distribution from which the variables are drawn.
In the context of the parameters you mentioned, approximate normality is often used when dealing with a distribution that has unknown or estimated parameters. In such cases, the mean (mu) is known or estimated, but the standard deviation (sigma) may be uncertain. To represent this uncertainty, the term "variation" that you mentioned is sometimes used to denote the estimated or approximate standard deviation.
So, to summarize, the normal distribution (X ~ N(mu, sigma)) is used when both the mean and standard deviation are known or assumed to be known. On the other hand, approximate normality (X ~ N(mu, variation)) is used when the mean is known but the standard deviation is estimated or uncertain.
It's important to note that while approximate normality can be a useful approximation in many cases, it is not always accurate, especially when dealing with small sample sizes or skewed distributions. In such situations, other distributions or statistical techniques may be more appropriate.