AP Statistics Flashcards: The Central Limit Theorem
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
What role does independence play in the Central Limit Theorem?
Independent sample values are a required condition for the Central Limit Theorem to be applicable.
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What role does independence play in the Central Limit Theorem?
Independent sample values are a required condition for the Central Limit Theorem to be applicable.
What are the two main requirements for the Central Limit Theorem to apply?
The CLT requires that the sample values are independent and that the sample size (n) is sufficiently large.
What key characteristic of the sampling distribution of the mean is described by the CLT?
The CLT describes the shape of the sampling distribution of the mean, stating that it will be approximately normal if the sample size is large enough.
If a researcher takes many large random samples from a non-normal population and plots the sample means, what shape will the resulting distribution have?
According to the Central Limit Theorem, the resulting sampling distribution of the mean will be approximately normal because the sample size is large.
How would you use simulation to understand the possible values of a sample statistic?
You would generate repeated random samples of a fixed size from a population to create an estimated sampling distribution of that statistic.
What is the relationship between a sampling distribution and a randomization distribution?
Both are distributions of a statistic generated through simulation, but a randomization distribution is created under the assumption of a known parameter.
Sufficiently Large Sample Size (n)
This is a key condition of the Central Limit Theorem required to ensure the sampling distribution of the mean is approximately normal.
How can sampling distributions be estimated using simulation?
Sampling distributions can be estimated by generating repeated random samples from a population and calculating the statistic for each sample.
What is a randomization distribution?
A randomization distribution is a collection of statistics that is generated by simulation assuming that known parameter values are true.
How is the simulation of a sampling distribution performed?
It is performed by generating repeated random samples from a population and compiling the values of the statistic calculated from each sample.
What is a sampling distribution of a statistic?
It is the distribution of values for a statistic that would be obtained from all possible samples of a given size from a population.
A study uses a small sample size (n=10) from a heavily skewed population. Why is it inappropriate to assume the sampling distribution of the mean is normal?
The Central Limit Theorem's requirement for a sufficiently large sample size has not been met, so the sampling distribution may not be approximately normal.
Does the Central Limit Theorem depend on the shape of the original population distribution?
No, as long as the sample size is sufficiently large, the sampling distribution of the mean will be approximately normal regardless of the population's distribution.
What is the Central Limit Theorem (CLT)?
The CLT states that for a large enough sample size, the sampling distribution of the mean will be approximately normal.