3.3StatisticsStretch

The Inverse Normal Distribution

The inverse normal function works backwards: given a probability, it finds the value of X that produces it. This answers questions like “what mark is the top 10% boundary?”.

22 min Video by Zeeshan Zamurred The Normal Distribution

Edexcel A Level Maths: 3.3 The Inverse Normal Distribution FunctionWatch the full walkthrough before the notes below.

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What you'll be able to do

Use the inverse normal function
Find a value of X from a probability
Handle “greater than” probabilities
Apply to percentile questions

Working backwards

Given $P (X < a) = p$ , the inverse normal function returns $a$ . Enter the probability (as area to the left), $μ$ and $σ$ .

P (X < a) = p \Rightarrow a = InvNorm (p, μ, σ)

From probability to value.

1InvNorm(0.9, 50, 4).

a \approx 55.1

Answer

a \approx 55.1

Tip — For “top 10%”, the area to the LEFT is 0.9 — convert before using InvNorm.

Formula recap

a = InvNorm (p, μ, σ)

Inverse normal (left area p).

P (X > a) = 0.1 \Rightarrow P (X < a) = 0.9

Convert tails.

Common mistakes to avoid

Entering a right-tail probability directly.

InvNorm uses the area to the LEFT — convert first.

Forgetting to enter μ and σ.

The function needs the distribution’s parameters.

Key takeaways

Inverse normal: given p, find a with P(X < a) = p.
Convert right-tail probabilities to left areas first.
Useful for percentile / boundary questions.

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