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.
See your most recent post.
You're on the right track, but let me clarify the differences between the normal distribution and approximate normal distribution.
The normal distribution, often referred to as the Gaussian distribution, is a probability distribution that is symmetric and bell-shaped. It is completely determined by two parameters: the mean (μ) and the standard deviation (σ). The notation for a variable X following a normal distribution is written as X ~ N(μ, σ).
On the other hand, the approximate normal distribution is an approximation of the normal distribution when certain conditions are met. This approximation is useful in situations where the sample size is large enough or when specific conditions are satisfied, such as the central limit theorem.
When using the approximate normal distribution, we often make use of the sample mean (x̄) and sample standard deviation (s) to estimate the parameters of the normal distribution. The notation for a variable X being approximately normally distributed is written as X ~ N(μ, s), where μ is the estimated mean and s is the estimated standard deviation.
In summary, the main difference lies in the parameters used. For the normal distribution, we know the exact values of the mean (μ) and standard deviation (σ), while for the approximate normal distribution, we estimate these values using the sample mean (x̄) and sample standard deviation (s). The approximate normal distribution is a useful tool for making inferences about a population based on sample data.