Given a probability and one parameter, work back to the missing μ or σ - a standard exam twist.
In short: Finding an unknown mean or standard deviation means using a given probability to work backwards through the normal distribution. You use inverse normal to find the boundary or z-value, then solve for the missing parameter. It is a common multi-mark question, so show the standardising step clearly alongside the GDC result.
| TI-84 Plus CE | Casio fx-CG50 and fx-CG100 | TI-Nspire CX | |
|---|---|---|---|
| Key sequence | invNorm(area-to-left, 0, 1) gives z; then solve z = (x − μ)/σ for the unknown. | DIST → NORM → InvN with μ = 0, σ = 1 gives z; substitute into z = (x − μ)/σ. | Use Inverse Normal with μ = 0, σ = 1 to get z, then solve the standardising equation for μ or σ. |
Tip: Sketch the curve and shade the area on the correct side before using invNorm.
Tip: Sketch the curve and shade the area on the correct side before using invNorm.
Tip: Sketch the curve and shade the area on the correct side before using invNorm.
Here's a real IB-style question that uses exactly this technique.
X ~ N(μ, 5²). Given that P(X < 20) = 0.2, find μ, to 3 significant figures.
Given a probability and one parameter, work back to the missing μ or σ - a standard exam twist. A question gives P(X < a) or P(X > a) and one of μ or σ, and asks you to find the other. Two probability statements are given and both μ and σ are unknown, needing simultaneous equations.
1. Turn the probability into a z-value using the inverse normal with μ = 0, σ = 1. 2. invNorm(area-to-left, 0, 1) gives z; then solve z = (x − μ)/σ for the unknown. 3. If two probabilities are given, form two equations and solve them simultaneously for μ and σ.
1. Turn the probability into a z-value using the inverse normal with μ = 0, σ = 1. 2. DIST → NORM → InvN with μ = 0, σ = 1 gives z; substitute into z = (x − μ)/σ. 3. If two probabilities are given, form two equations and solve them simultaneously for μ and σ.
1. Turn the probability into a z-value using the inverse normal with μ = 0, σ = 1. 2. Use Inverse Normal with μ = 0, σ = 1 to get z, then solve the standardising equation for μ or σ. 3. If two probabilities are given, form two equations and solve them simultaneously for μ and σ.
Sketch the curve and shade the area on the correct side before using invNorm.
In the worked example on this page (4 marks, Paper 2), the marks are: M1: Find the z-value with invNorm(0.2, 0, 1); M1: Set up 20 = μ + z(5) and solve for μ; A1: μ = 24.2.
Questions that need this technique link back to this guide. Try one in practice mode, or see every GDC guide.