Unit 4: Statistics and Probability
Topic 4.12: Standardized Normal and Inverse Questions
Practice 16 exam-style questions for IB Math AA SL Topic 4.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Explain1 mark
2026• Aimnova practice — 4.12.1
Explain what it means for a data value to have a z-value of 0.
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2026• Aimnova practice — 4.12.1
X ~ N(80, 12²). Find the z-value of x = 62.
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2026• Aimnova practice — 4.12.1
X ~ N(50, 6²). Find the z-value of x = 62.
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2026• Aimnova practice — 4.12.1
X ~ N(25, 4²). A value has a z-value of 1.75. Find x.
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2026• Aimnova practice — 4.12.2
X ~ N(200, 25²). Find the value x such that P(X < x) = 0.85.
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2026• Aimnova practice — 4.12.1
In Maths (mean 65, sd 10) a student scores 80; in Physics (mean 70, sd 5) they score 79. In which subject did they do better relative to the class?
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2026• Aimnova practice — 4.12.2
Exam marks are X ~ N(58, 12²). The top 15% receive a distinction. Find the minimum mark for a distinction.
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2026• Aimnova practice — 4.12.1
A normally distributed value has z = −1.2, mean 100 and standard deviation 15. Find the value x.
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2026• Aimnova practice — 4.12.2
X ~ N(60, 8²). Find x such that P(X > x) = 0.1.
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2026• Aimnova practice — 4.12.1
A value in X ~ N(40, σ²) has z = 2.5 and equals 55. Find σ.
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2026• Aimnova practice — 4.12.2
X ~ N(40, 5²). Find the two values between which the central 90% of the data lies.
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2026• Aimnova practice — 4.12.2
Reaction times are X ~ N(μ, 0.05²) s. The fastest 10% react in under 0.28 s. Find μ.
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2026• Aimnova practice — 4.12.1
Two athletes' times are standardised. Sprinter P has z = −1.8 and sprinter Q has z = −0.5 (lower time is better). State who performed better relative to their field, with a reason.
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2026• Aimnova practice — 4.12.2
Heights are X ~ N(μ, 6²) cm. Given P(X > 180) = 0.2, find μ.
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2026• Aimnova practice — 4.12.2
Lifetimes are X ~ N(800, σ²) hours. Given that 25% last less than 740 hours, find σ.
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2026• Aimnova practice — 4.12.2
Bottles are filled to X ~ N(500, σ²) ml. Given P(X < 488) = 0.05, find σ.
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