Sampling Distributions for Sample Proportions

Sampling Distributions for Sample Proportions is topic 5.5 of AP Statistics, inside Sampling Distributions. This page works through three real practice questions on it, with the full reasoning behind each credited answer.

Practise this topic freeThe whole unit
49 questionsStatistical Argumentation100% with a figure
Worked examples

Three real sampling distributions for sample proportions questions

From the practice pool, not the mock papers — each with the reasoning that produces the answer.

100% of them come with a figure. Reading the graph or diagram correctly is most of the work here before any content knowledge applies.

96% test a single AP skill: Statistical Argumentation. That makes this topic unusually predictable to prepare for.

Statistical Argumentation · with figure

For random samples of size 180, suppose p = 0.09 for sample boxes converted to orders. Which check addresses whether p-hat is approximately normal?

  1. AOnly 180 > 30 must be checked.
  2. BUse sqrt(p(1-p))
  3. COnly p = 0.09 must be checked.
  4. D180(0.09) = 16.2 and 180(0.91) = 163.8correct
  5. EThe check requires exactly 10 observed successes.
Why D is correct

Check np and n(1-p): 180(0.09) = 16.2 and 180(0.91) = 163.8.

large-count check for sample boxes converted to orders: in the "For random samples of size 180, suppose p = 0.09 for sample boxes converted to orders. Which check addresses whether p-hat is approximately normal?" setting, especially sample boxes converted to orders; trial conversions, identify the sampling-distribution center, spread, and conditions before using a model. The professional check is to keep the values 180, 0.09, the sample proportion normal condition method, and the final answer choice aligned with Sampling Distributions.

Statistical Argumentation · with figure

For random samples of size 120, suppose p = 0.14 for delayed catering orders. Which check addresses whether p-hat is approximately normal?

  1. AUse sqrt(p(1-p))
  2. BOnly 120 > 30 must be checked.
  3. COnly p = 0.14 must be checked.
  4. DThe check requires exactly 10 observed successes.
  5. E120(0.14) = 16.8 and 120(0.86) = 103.2correct
Why E is correct

Check np and n(1-p): 120(0.14) = 16.8 and 120(0.86) = 103.2.

large-count check for delayed catering orders: in the "For random samples of size 120, suppose p = 0.14 for delayed catering orders. Which check addresses whether p-hat is approximately normal?" setting, especially delayed catering orders; returns, identify the sampling-distribution center, spread, and conditions before using a model. The professional check is to keep the values 120, 0.14, the sample proportion normal condition method, and the final answer choice aligned with Sampling Distributions.

Statistical Argumentation · with figure

For random samples of size 70, suppose p = 0.52 for donors choosing monthly giving. Which check addresses whether p-hat is approximately normal?

  1. A70(0.52) = 36.4 and 70(0.48) = 33.6correct
  2. BOnly p = 0.52 must be checked.
  3. CThe check requires exactly 10 observed successes.
  4. DUse sqrt(p(1-p))
  5. EOnly 70 > 30 must be checked.
Why A is correct

Check np and n(1-p): 70(0.52) = 36.4 and 70(0.48) = 33.6.

large-count check for donors choosing monthly giving: in the "For random samples of size 70, suppose p = 0.52 for donors choosing monthly giving. Which check addresses whether p-hat is approximately normal?" setting, especially donors choosing monthly giving; bilingual audio, identify the sampling-distribution center, spread, and conditions before using a model. The professional check is to keep the values 70, 0.52, the sample proportion normal condition method, and the final answer choice aligned with Sampling Distributions.

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Last reviewed 2026-08-28. Topic and unit names follow the College Board course framework. Question counts describe the PrepScore practice bank, not the exam.

Work sampling distributions for sample proportions until the reasoning is automatic.

Real AP questions with a full explanation on every answer, and a mistake bank that only clears when you get it right.

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