The reverse of a normal probability: given a percentage, find the cut-off value (e.g. the mark for the top 10%).
In short: Inverse normal works backwards from a probability to a value: it returns the x-value below which a given area of a normal distribution lies. You enter the area to the left, the mean and the standard deviation. Use it for questions that give a percentage or probability and ask for a boundary value.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | 2nd → VARS (DISTR) → invNorm(area, μ, σ). Newer OS lets you pick the tail. | Main menu → Statistics → DIST → NORM → InvN; set the tail and enter area, σ, μ. | menu → Probability → Distributions → Inverse Normal; enter the area, μ and σ. |
Tip: invNorm needs the area to the LEFT. For "top 10%", use area = 0.90; for "bottom 25%", use area = 0.25.
Tip: invNorm needs the area to the LEFT. For "top 10%", use area = 0.90; for "bottom 25%", use area = 0.25.
Tip: invNorm needs the area to the LEFT. For "top 10%", use area = 0.90; for "bottom 25%", use area = 0.25.
Here's a real IB-style question that uses exactly this technique.
Test scores are modelled by X ~ N(60, 10²). Find the score k such that P(X > k) = 0.1, to 3 significant figures.
The reverse of a normal probability: given a percentage, find the cut-off value (e.g. the mark for the top 10%). A question gives a probability (or percentage) and asks you to find the corresponding value. Finding a cut-off, e.g. the mark needed to be in the top 10% of a normally distributed set of results.
1. Work out the area to the LEFT of the value you want. 2. 2nd → VARS (DISTR) → invNorm(area, μ, σ). Newer OS lets you pick the tail.
1. Work out the area to the LEFT of the value you want. 2. Main menu → Statistics → DIST → NORM → InvN; set the tail and enter area, σ, μ.
1. Work out the area to the LEFT of the value you want. 2. menu → Probability → Distributions → Inverse Normal; enter the area, μ and σ.
invNorm needs the area to the LEFT. For "top 10%", use area = 0.90; for "bottom 25%", use area = 0.25.
In the worked example on this page (3 marks, Paper 2), the marks are: M1: invNorm(0.9, 60, 10), using P(X < k) = 0.9; A1: k = 72.8.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.