How it works
This AP Statistics sampling distributions practice test has 51 questions of our own on the central limit theorem and on the sampling distributions of proportions, means and their differences. It is unofficial and not affiliated with the College Board.
Read the full guide
Where sampling distributions sit now
The College Board revised AP Statistics for the 2026-27 school year. Its course description, effective fall 2026 and read October 11, 2026, has five units and none named Sampling Distributions. The bank follows the topics that hold the material: 2.12 (10 questions), 3.1 and 3.2 on sample proportions (14), 4.1 on sample means (13), and 3.9 and 4.6 on differences (14). The description gives topics no weights, so the spread is ours.
How the answers are checked
Each rule is cited to an essential knowledge statement of the course description or to a Wikipedia article, and every worked answer was recomputed from the numbers in its question.
- Say which distribution you mean: the population, the data in one sample, or a statistic over repeated samples.
- For proportions, check np and n(1 - p) are both at least 10. For means from a non-normal population, check n is at least 30.
- Four times the sample size halves the standard deviation of a sample mean or a sample proportion.
Questions and answers
What unit is sampling distributions in AP Statistics?
In the older framework of nine units it was the fifth, Sampling Distributions. The description effective fall 2026 has five units and spreads the material over Unit 2 (topic 2.12), Unit 3 (3.1, 3.2, 3.9) and Unit 4 (4.1, 4.6).
What does an AP Stat sampling distribution practice test cover?
Simulating a sampling distribution, the central limit theorem, unbiased estimators, and the mean, the standard deviation and the conditions for a normal model for a sample proportion, a sample mean and the difference of two of each.
What is a sampling distribution?
The distribution of the values a statistic takes over all possible samples of one size from one population. It is not the population, and it is not the data in a single sample.
When is a sampling distribution approximately normal?
For a sample proportion, when np and n(1 - p) are both at least 10. For a sample mean, when the population is normal or n is at least 30; an extremely skewed population may need a much larger sample.
Are these real AP Statistics exam questions?
No. The College Board owns the real questions, and none appears here, even in other words. Every question was written for this page from the topics the course description lists.