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IB Maths AI HL Ahl 4 15 Hl Sampling Distributions and Clt Questions

Practise using sampling distributions and the central limit theorem to calculate probabilities or intervals for means, combining independent normal variables.

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

Exam points

  • Use the distribution of a sample mean for normal populations, including the variance reduction σ²/n.
  • Apply the central limit theorem for sufficiently large samples and calculate probabilities or intervals for X̄.
  • Combine independent normal variables and interpret the sampling-distribution result in context.

IB Maths AI HL Ahl 4 15 Hl Sampling Distributions and Clt Questions question 1

[Maximum number: 4]

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.

Taylor intends to play the game for one hour.

Use the central limit theorem to find the probability that Taylor's mean score per minute is greater than 25 .

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