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What is a z score and what its used for?
The Normal probability distribution is defined by two parameters: its mean and standard deviation (sd) and, between them, these two can define infinitely many different Normal distributions. The Normal distribution is very common but there is no simple way to use it to calculate probabilities. However, the probabilities for the Standard Normal distribution (mean = 0, sd = 1) have been calculated numerically and are tabulated for quick reference. The z-score is a linear transformation of a Normal variable and it allows any Normal distribution to be converted to the Standard Normal. Finding the relevant probabilities is then a simple task.
What are the advantages of using the standard normal distribution over the normal distribution?
There is no simple formula to calculate probabilities for the normal distribution. Those for the standard normal have been calculated by numerical methods and then tabulated. As a result, probabilities for the standard normal can be looked up easily.
What is z value?
If a random variable (RV) X is distributed Normally with mean m and standard deviation sthenZ = (X - m)/s is the corresponding Normal variable which is distributed with mean 0 and variance 1. The distribution of X is difficult to compute but that for Z is readily available. It can be used to find the probabilities of the RV lying in different domains and thereby for testing hypotheses.
Why does a researcher want to go from a normal distribution to a standard normal distributio?
A normal distribution simply enables you to convert your values, which are in some measurement unit, to normal deviates. Normal deviates (i.e. z-scores) allow you to use the table of normal values to compute probabilities under the normal curve.
What is a normal random variable minus its mean and divided by its standard deviation?
It is the Standard normal variable.
