Unit 4: Statistics and Probability
Topic 4.8: Binomial Distribution Questions
Practice 16 exam-style questions for IB Math AA SL Topic 4.8. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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2026• Aimnova practice — 4.8.2
A fair coin is tossed 64 times. Find the expected number of heads and the standard deviation of the number of heads.
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2026• Aimnova practice — 4.8.2
X ~ B(40, 0.15). Find the mean and the variance.
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2026• Aimnova practice — 4.8.2
A spinner lands on red with probability 0.45. It is spun 200 times. Find the expected number of reds and the variance.
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2026• Aimnova practice — 4.8.1
X ~ B(20, 0.35). Find P(X ≤ 6).
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2026• Aimnova practice — 4.8.1
X ~ B(15, 0.2). Find P(X = 3).
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2026• Aimnova practice — 4.8.2
A binomial variable has mean 18 and variance 7.2. Find n and p.
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2026• Aimnova practice — 4.8.2
In a large batch, 8% of items are defective. A sample of 150 is taken. Find the expected number of defective items and the standard deviation.
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2026• Aimnova practice — 4.8.2
For X ~ B(n, 0.25), the mean is 15. Find n and the variance.
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2026• Aimnova practice — 4.8.1
X ~ B(25, 0.3). Find P(5 ≤ X ≤ 9).
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2026• Aimnova practice — 4.8.2
A binomial variable X has E(X) = 9 and Var(X) = 6.3. Find n and p, then state X ~ B(n, p).
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2026• Aimnova practice — 4.8.2
X ~ B(100, 0.3). Find the standard deviation.
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2026• Aimnova practice — 4.8.1
A fair die is rolled 8 times. Find the probability of getting at least one six.
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2026• Aimnova practice — 4.8.1
A multiple-choice quiz has 10 questions, each with 4 options; a student guesses every answer. Find the probability of getting exactly 3 correct.
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2026• Aimnova practice — 4.8.1
In a town, 60% of households recycle. In a random sample of 18 households:
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2026• Aimnova practice — 4.8.1
X ~ B(12, 0.4). Find P(X ≥ 5).
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2026• Aimnova practice — 4.8.1
Each chocolate has a winning wrapper with probability 0.15. How many must be bought so that P(at least one winner) is at least 0.95?
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