L3 Probability Distributions Past Papers
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AS91586Probability Distributions past exam papers
Every NZQA exam for AS91586 (Apply probability distributions in solving problems) from 2013 to 2025, with its marking schedule, and from 2020 the examiners’ report, which says where students lost marks.
Papers by year
2020Archived copy
2019Archived copy
2018Archived copy
2017Archived copy
2016Archived copy
2015Archived copy
2014Archived copy
2013Archived copy
Marked student answers at each grade (NZQA exemplars), 2024: Achievement · Merit · Excellence.
What the examiners keep saying
Always name the distribution and its parameters, and show your working. The wrong distribution can give a similar number, so a bare answer can earn nothing.
Reports: 2021–2025Define the random variable in context, then choose which distribution fits. In 2021 many students seemed to know only one distribution and used it for everything.
Reports: 2021–2025Keep at least four decimal places, or exact fractions, until the end: 1/3 is not 0.33. Rounding too early is on the Not Achieved list every year.
Reports: 2021–2025Give a distribution’s conditions in terms of the situation, and don’t borrow another distribution’s conditions. For a Poisson model they are independent events at a constant average rate; “rare” and “counts” are only hints.
Reports: 2021–2025Judge whether a model fits by comparing the data’s graph with the model, using relative frequencies, in context. Since 2024 the reports also want you to judge whether its parameters are right.
Reports: 2021–2025Merit needs the multi-step problems: a conditional probability within a distribution, or working back to a parameter such as λ or σ from a given probability.
Reports: 2021–2025The Achievement basics: the mean and standard deviation from a probability table, and a proportion read off a frequency graph to test a claim.
Reports: 2021–2025Know the difference between conditions and assumptions, and say whether your assumptions are reasonable even when the question doesn’t ask.
Reports: 2021, 2022, 2023 and 2025
How to use these papers
- Start with the most recent papers. They are the closest to this year’s exam.
- Sit a whole paper without notes, then mark it with its schedule. The schedule shows what earns Achievement, Merit and Excellence in each part, not only the answer.
- After marking, read that year’s examiners’ report to see where other students lost marks.
- Check the 2026 assessment specification for what this year’s exam covers. An older paper can include something that has since changed.
About the older papers
NZQA takes papers off its website after five years. The older ones here are NZQA’s own files as saved by the Internet Archive, a non-profit library of the web, so they can be slow to open. We could only find the examiners’ reports from 2020 on.
Practise each topic in AS91586 with worked answers.
Open the Probability Distributions question bank →