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 => P( Z < (x_0-\mu)/sigma) = T #

#=> (x_0 -\mu)/sigma = # InvNorm(T)

Then #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