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IB Maths AI HL Ahl 4 17 Hl Poisson Distribution Questions

Practise choosing and applying a Poisson model, calculating probabilities, comparing alternative distributions and interpreting the rate or count context.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Choose a Poisson model and identify its mean/variance parameter from a rate or count context.
  • Calculate Poisson probabilities and use the fact that sums of independent Poisson variables remain Poisson.
  • Compare normal, binomial and Poisson models and justify the appropriate choice and interpretation.

Learn this topic

Study AHL 4.17 (HL)—Poisson distribution conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI HL Ahl 4 17 Hl Poisson Distribution Questions question 1

[Maximum number: 6]

Taylor is playing a computer game in which they shoot at spaceships and battleships. The number of spaceships they hit per minute can be modelled by a Poisson distribution with mean 4.2. The number of battleships they hit per minute can be modelled by a Poisson distribution with a mean of 2.3. Any single hit occurs independently of all others.

Question (a)

(a)

Find the probability Taylor hits

[ 5 ]

Question (i)

(i)

at most 10 spaceships in 2 minutes.

[ 2 ]

Question (ii)

(ii)

a total of more than 10 spaceships and battleships in one minute.

[ 3 ]

Question (b)

(b)

State one reason why the distribution of T cannot be Poisson.

[ 1 ]
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