Unit 4: Statistics and Probability
Topic 4.9: Normal Distribution Questions
Practice 16 exam-style questions for IB Math AA SL Topic 4.9. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
1Find2 marks
2026• Aimnova practice — 4.9.1
X ~ N(20, 4²). Find P(X > 26).
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2026• Aimnova practice — 4.9.2
X ~ N(72, σ²). Write down P(X < 72) and P(X > 72).
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2026• Aimnova practice — 4.9.2
Sketch a normal curve for X ~ N(20, 3²) and describe the region representing P(X < 17).
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2026• Aimnova practice — 4.9.1
Battery lifetimes are X ~ N(500, 50²) hours. Find the probability a battery lasts less than 560 hours.
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2026• Aimnova practice — 4.9.1
X ~ N(20, 4²). Find P(14 < X < 24).
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2026• Aimnova practice — 4.9.1
The contents of a bottle are X ~ N(330, 4²) ml. A bottle is underfilled if it holds less than 325 ml. Find the percentage of bottles that are underfilled.
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2026• Aimnova practice — 4.9.2
On one diagram, two normal curves have means 30 and 45 with the same standard deviation. Describe how the two curves are related.
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2026• Aimnova practice — 4.9.2
The lifetimes of two bulb types are normal with the same mean. Type X has a wider, flatter curve than Type Y. Compare their standard deviations and reliability.
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2026• Aimnova practice — 4.9.2
Two machines fill bottles to a normal distribution with the same mean. Machine A has σ = 2 ml and Machine B has σ = 6 ml. State which machine is more consistent, and describe the difference in their curves.
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2026• Aimnova practice — 4.9.1
The times to finish a race are X ~ N(75, 8²) minutes. Find the probability a runner finishes between 65 and 85 minutes.
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2026• Aimnova practice — 4.9.1
Packet masses are X ~ N(3.4, 0.5²) kg. In a delivery of 200 packets, find the expected number heavier than 4 kg.
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2026• Aimnova practice — 4.9.1
IQ scores are X ~ N(100, 15²). Find the probability a person scores between 85 and 130.
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2026• Aimnova practice — 4.9.2
A normal distribution has mean 50. Given P(X < 42) = 0.2, find P(X > 58).
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2026• Aimnova practice — 4.9.2
A normal distribution has mean 100. Given P(X > 115) = 0.15, find P(85 < X < 115).
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2026• Aimnova practice — 4.9.1
A normal distribution has mean 60 and standard deviation 5. Using the empirical rule, estimate P(55 < X < 65) and P(X > 65).
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2026• Aimnova practice — 4.9.2
A normal curve has mean μ and standard deviation σ. Explain why P(X > μ + 2σ) is small.
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