That is, \(z\) only follows a standard normal distribution if \(x\) is normally distributed. Standardizing values does not “normalize” them in any way. However, this is exactly what happens if we run a t-test or a z-test. So if \(x\) follows a normal distribution then \(z\) follows a standard normal distribution.Ĭonverting \(x\) into \(z\) may seem theoretical. The result of doing so is that \(z\) is given a standard of μ = 0 and σ = 1. With these 3 numbers we could also compute a z-score: we know its population standard deviation σ.Why? Well, we can use a normal distribution to look up a probability for \(x\) if The standard normal distribution is the only normal distribution we really need. The normal distribution is the probability density function defined by Finding Critical Values from an Inverse Normal Distribution.Finding Probabilities from a Normal Distribution.Normal Distribution – Quick Introduction By Ruben Geert van den Berg under Statistics A-Z
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