AP Statistics Flashcards: Sampling Distributions for Sample Means
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.
A population has a mean (mu) of 75 and a standard deviation (sigma) of 12. For random samples of size n=36, what are the parameters of the sampling distribution of x-bar?
The mean of the sampling distribution is 75, and the standard deviation is sigma/sqrt(n) = 12/sqrt(36) = 2.
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A population has a mean (mu) of 75 and a standard deviation (sigma) of 12. For random samples of size n=36, what are the parameters of the sampling distribution of x-bar?
The mean of the sampling distribution is 75, and the standard deviation is sigma/sqrt(n) = 12/sqrt(36) = 2.
A population distribution is heavily skewed right. Can we describe the sampling distribution of the sample mean as approximately normal if our sample size is n=100?
Yes, because the sample size (n=100) is large enough (n >= 30), the Central Limit Theorem states the sampling distribution will be approximately normal.
What is the 10% condition and why is it important for sample means?
When sampling without replacement, the sample size should be less than 10% of the population to ensure the standard deviation formula (sigma/sqrt(n)) is approximately correct.
What are the two distinct conditions that allow us to describe a sampling distribution of a sample mean as approximately normal?
The sampling distribution is approximately normal if either the original population distribution is normal, or if the sample size is large enough (n >= 30).
Why is it critical to interpret probabilities and parameters for a sampling distribution in context?
Interpreting probabilities and parameters in context is essential for conveying the practical meaning and significance of the statistical findings.
Under what condition is the sampling distribution of the sample mean (x-bar) guaranteed to be normal?
If the population distribution is normal, the sampling distribution of the sample mean is also normal, regardless of the sample size.
What is the Central Limit Theorem (CLT) condition for the sampling distribution of a sample mean?
If the population distribution is not normal, the sampling distribution of the sample mean is approximately normal if the sample size is large enough (e.g., n >= 30).
What two parameters are needed to determine the sampling distribution for a sample mean?
The two parameters are the mean (mu) and the standard deviation (sigma/sqrt(n)) of the sampling distribution.
If the probability of observing a sample mean less than 5 minutes is 0.02, how should this result be interpreted?
This probability should be interpreted in the context of the specific problem, stating there is a 2% chance of getting a sample mean less than 5 minutes.
What is the formula for the standard deviation of the sampling distribution of the sample mean (x-bar)?
The standard deviation of the sampling distribution of the sample mean is the population standard deviation divided by the square root of the sample size (sigma/sqrt(n)).
How does increasing the sample size (n) affect the standard deviation of the sampling distribution of the sample mean?
Increasing the sample size (n) decreases the standard deviation of the sampling distribution, as n is in the denominator of the formula (sigma/sqrt(n)).
What is the mean of the sampling distribution of the sample mean (x-bar)?
The mean of the sampling distribution of the sample mean is equal to the population mean (mu).
What is the rule of thumb for a sample size to be considered 'large enough' for the Central Limit Theorem to apply to sample means?
A sample size (n) is generally considered large enough if it is greater than or equal to 30 (n >= 30).
A population distribution is heavily skewed left. Can we describe the sampling distribution of the sample mean as approximately normal if our sample size is n=20?
No, because the population is not normal and the sample size (n=20) is not large enough (less than 30) for the Central Limit Theorem to apply.