Statistics

Inverse Normal

Inverse normal calculations work backwards from probability to a value of \(x\).

Forward vs inverse normal

Question typeWhat you knowWhat you find
Normal CDFA value of \(x\)A probability / area
Inverse normalA probability / areaA value of \(x\)

Worked example

Let \(X\sim N(50,8^2)\). Find the value \(k\) such that \(P(X

  1. Use inverse normal with area \(0.9\), mean \(50\), standard deviation \(8\).
  2. Equivalently, \(z\approx1.282\).
  3. So \(k=50+1.282(8)\approx60.3\).

Calculator tip

Check whether your calculator asks for left-tail area, right-tail area, or a central area. Most IB calculator workflows use left-tail cumulative probability.

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