Work out inverse normal distribution instantly with clear inputs, formula shown and shareable results.
The inverse normal, or quantile function, answers the reverse question: which value has a given proportion of the distribution below it. Finding z first and then scaling by σ and shifting by μ gives the answer.
Inverse normal
x = μ + σ·Φ⁻¹(p)
z = 1.96, so x = 100 + 29.4 = 129.4 — the classic IQ threshold for the top 2.5%.
Φ has no elementary inverse, so rational approximations such as Acklam's are used, accurate to about 10⁻⁹.