This ap statistics sampling distributions quiz asks 10 multiple-choice questions on sampling distributions, and each answer comes with a short explanation.
Ten multiple-choice questions check the central ideas of sampling distributions: the mean and standard deviation of a sample proportion and a sample mean, the effect of sample size, the Central Limit Theorem, bias and variability, and differences. Each question has one correct answer; read the explanation after you choose.
AP StatisticsCommon Core: AP Statistics Unit 2 (2026-27)
🎯 Sampling Distributions – AP Statistics math quiz
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Question 1
A random sample of 80 students is taken from a school where 30% play sports. What is the mean of the sampling distribution of the sample proportion?
A0.30
B0.30 divided by 80
C24
D0.0512
Question 2
For p = 0.2 and n = 100, what is the standard deviation of the sample proportion?
A0.4
B0.04
C0.0016
D0.16
Question 3
A sample size is multiplied by 4. What happens to the standard deviation of the sample mean?
AIt is divided by 4
BIt is multiplied by 2
CIt stays the same
DIt is divided by 2
Question 4
The curves show sampling distributions of a sample proportion from the same population for n = 100 and n = 400. Which statement is correct? Blue is wide, orange is narrow.
AThe narrow curve is n = 100 because smaller samples vary less
BThe narrow curve is n = 400 because larger samples vary less
CThe wide curve is n = 400 because larger samples vary more
DThe curves differ in center because the sample sizes differ
Question 5
When is the sampling distribution of the sample mean approximately normal for a strongly skewed population?
AWhen n = 10
BWhen n = 5
CWhen n = 50
DNever, because the population is skewed
Question 6
A population has standard deviation 15. What is the standard deviation of the sample mean for n = 25?
A0.6
B15
C3
D75
Question 7
The dot plots show sample proportions from three methods for estimating p = 0.40 (dashed line). Which method has low bias and low variability? Methods A, B and C.
AMethod B
BMethod C
CAll three methods
DMethod A
Question 8
Sample 1: sigma = 6, n = 36. Sample 2: sigma = 8, n = 64. What is the standard deviation of the difference of sample means?
A1.41
B2.00
C0.29
D1.00
Question 9
The sampling distribution of a sample proportion is approximately normal with mean 0.50 and standard deviation 0.05. What is the shaded area, P(p-hat < 0.45)? Shaded area left of 0.45.
A0.8413
B0.3174
C0.1587
D0.0500
Question 10
Two independent samples have p1 = 0.70 and p2 = 0.55. What is the mean of the sampling distribution of the difference of sample proportions?
A0.15
B1.25
C0.385
D0.0225
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Sample proportion: \(\mu_{\hat{p}}=p\), \(\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}\); normal when \(np\ge 10\) and \(n(1-p)\ge 10\).
Sample mean: \(\mu_{\,\overline{x}}=\mu\), \(\sigma_{\,\overline{x}}=\frac{\sigma}{\sqrt{n}}\); approximately normal if the population is normal or \(n\ge 30\) (Central Limit Theorem).
The standard-deviation formulas need independence: \(n\le 10\%\) of the population when sampling without replacement.
Random sampling gives unbiased statistics; a larger \(n\) reduces variability, and quadrupling \(n\) halves the standard deviation.
For differences, the means subtract but the variances add.
How to use this ap statistics sampling distributions quiz
Retake this ap statistics sampling distributions quiz until every answer is right, then move on to the worksheet and the test.
