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Anytime you aim to perform a study on the entire population, you will surely find that this task will be: Much time and/or efforts consuming as populations are normally huge . Impossible if the population is infinite (such as products). Here comes the role of taking samples. Yes! we just take a sample from the whole population, perform the study on the chosen sample, apply the results back to our population. This is the core of inferential statistics because what we do is to infer parameters/properties of the population using information from a small sample. Well, this does not mean we will obtain 100% exact accurate estimations or inferences. But to be as close as possible, sample elements should be taken randomly ! At least, being random in sample selection will mostly include the diversity of information/facts within our population.
You mostly know: the Standard Normal Distribution is the special case of Normal Distribution, given that: Mean: Mu=0.0 Variance: Sigma^2=1.0 Cool, as shown below: the family of normal distributions mainly vary in their mean value and/or their variance. The standard one plays the role of being the reference distribution. Well, we can convert any normal random variable to corresponding interpretations in the standard form. Hence, we simplify different computations only using standard normal distribution. OK, let's assume X is a normal distribution with mean Mu and variance Sigma^2. We can convert to a standard normally distributed random variable by following: Z=(X-Mu)/Sigma Here, we got Z as the standard normal distribution. OK, but what does this mean? Any point in X (with Mu, Sigma ) can be dealt exactly as the converted point in Z with mean Mu=0.0 and Sigma=1.0 . The numerator means: how much is the distance or differe...
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