Unit 4: Statistics and Probability
Topic 4.17: Poisson distribution (HL only) Questions
Practice 14 exam-style questions for IB Math AI SL Topic 4.17. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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A Poisson distribution has variance 9. Its mean is:
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Write down the variance of the number of calls in one minute.
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For X ~ Po(4), the value of P(X = 0) is:
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A bakery sells gluten-free loaves at an average of 2.5 per day, modelled by X ~ Po(2.5). Find P(X = 4) for a given day.
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Which situation is best modelled by a Poisson distribution?
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Customers enter a shop at an average of 6 per hour, modelled by a Poisson distribution. Find the expected number AND the standard deviation of the number of customers in one hour.
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X ~ Po(1.2) and Y ~ Po(2.8) are independent. P(X + Y = 0) equals:
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To find P(X ≥ 4) for X ~ Po(m) on the GDC, you compute:
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Find the probability of exactly two calls in a minute, and of at least five.
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Emails arrive at a small office at a mean rate of 3.2 per hour, modelled by a Poisson distribution. Find the probability that more than 5 emails arrive in a given hour.
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Find the mean over a two-minute period, the probability of exactly five calls in two minutes, and the probability of no calls in a thirty-second period.
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A factory records the number of machine breakdowns per week over many weeks: the sample mean is 2.9 and the sample variance is 2.8. Comment on whether a Poisson model is suitable.
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Typing errors occur at a mean of 0.4 per page, modelled by a Poisson distribution. A document is 8 pages long.
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At a reserve, deer are seen at a mean of 1.8 per hour and foxes at 0.5 per hour, independently, each Poisson. Find the probability of exactly 2 animals (deer or foxes) seen in one hour.
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