Unit 4: Statistics and Probability
Topic 4.9: Normal Distribution Questions
Practice 20 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.
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The times to finish a cycling stage are minutes. Find .
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, where has not been given. Write down .
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The lengths of a type of nail are millimetres. Write down , correct to two significant figures.
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Two normal curves drawn on one pair of axes have means 25 and 40 and equal standard deviations. Describe how the curves are related.
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X ~ N(72, σ2). Write down P(X < 72) and P(X > 72).
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Sketch a normal curve for and describe the region representing .
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2025
The masses of apples are normally distributed with mean 50 g and standard deviation 4 g. It is known that P(X > k) = 0.2.
Sketch a normal curve showing this information, marking 50 and k.
Sketch a normal curve showing this information, marking 50 and k.
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2025
The random variable Z has a standard normal distribution. It is known that P(−1.2 < Z < b) = 0.6.
Sketch a normal curve showing this information, marking −1.2 and b.
Sketch a normal curve showing this information, marking −1.2 and b.
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2026
Battery lifetimes are hours. Find the probability a battery lasts less than 560 hours.
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Sketch a normal curve for X ~ N(20, 32) and describe the region representing P(X < 17).
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X ~ N(20, 42). Find P(14 < X < 24).
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Battery lifetimes are X ~ N(500, 502) hours. Find the probability a battery lasts less than 560 hours.
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A waiting time, in minutes, is . Using the empirical rule, write down an estimate of .
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A normal distribution has mean 40, and . Find .
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