How do you find the z score of a percentile?

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Answer 1 · 2018-01-31T19:16:10

Z = (x - mean)/standard deviation.

Assuming that the underlying distribution is normal, we can construct a formula to calculate z-score from given percentile T%.

$P (X < x_{0}) = T \Rightarrow P (Z < \frac{x_{0} - μ}{σ}) = T$ $P(X<x_0) = T => P( Z < (x_0-\mu)/sigma) = T$

$\Rightarrow \frac{x_{0} - μ}{σ} =$ $=> (x_0 -\mu)/sigma =$ InvNorm(T)

Then $z = \frac{x_{0} - μ}{σ} =$ $z = (x_0-\mu)/sigma =$ InvNorm(T)

Note that InvNorm(T) is a TI function, similarly we can use excel function Norm.Inv(T, 0, 1)

For example, z-score of 30th percentile is InvNorm(0.3) = -0.52