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Grade 7 · unit review

Review: Sampling and Compound Chance

A complete population, a selected sample and a probability model are different sources of information. Sampling supports estimates, observed trial counts support experimental proportions, and explicit independence permits multiplication of model probabilities.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. A fictional school has 140 students on one roster. Which plan is a simple random sample of 20 students?
Need a hint?
  • A simple random sample can be created by selecting distinct random identifiers from a complete roster.
  • Random selection requires an actual procedure rather than a claim that volunteers seem varied.
2. In a random sample of 40 from a fictional population of 400, 25 favor a proposal. Use the sample proportion to estimate the population number favoring it.
Need a hint?
  • A sample proportion divides the counted category by the sample size.
  • An estimate is not a census total.
3. A model trial succeeds 10 times in 40 attempts. What is the experimental success proportion?
Need a hint?
  • An experimental proportion describes successful outcomes in a supplied trial record.
  • A small supplied record does not guarantee the next outcome.
4. A fair coin and a fair 8-section spinner are independent. What is the chance of heads and section 1?
Need a hint?
  • Independent events have a joint probability equal to the product of their individual probabilities.
  • Independence is a stated assumption here, not something true of every pair of events.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. A fictional school has 180 students on one roster. Which plan is a simple random sample of 20 students? Candidate answers: (A) Ask 20 members of the chess club (B) Ask the first 20 students entering the library (C) Assign every roster member a number; randomly select 20 different numbers (D) Choose 20 students whose names you recognize. 2. In a random sample of 40 from a fictional population of 400, 27 favor a proposal. Use the sample proportion to estimate the population number favoring it. Candidate answers: (A) 269 people (B) 270 people (C) 271 people (D) 540 people. 3. A model trial succeeds 12 times in 40 attempts. What is the experimental success proportion? Candidate answers: (A) 10/3 (B) 3/10 (C) 3/7 (D) 7/10. 4. A fair coin and a fair 10-section spinner are independent. What is the chance of heads and section 1? Candidate answers: (A) 1/10 (B) 1/2 (C) 1/20 (D) 3/5.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. Assign every roster member a number; randomly select 20 different numbers. Random selection from the complete roster gives each roster member the same selection chance. Convenience or one-club samples can underrepresent other students. 2. 270 people. The sample proportion is 27/40. Multiply by 400: (27/40)×400=270. This is an estimate with sampling variation, not an exact count. 3. 3/10. Divide observed successes by all attempts: 12/40=3/10. This proportion describes the supplied record and does not guarantee future trial results. 4. 1/20. Heads has chance 1/2 and the named section has chance 1/10. Independence permits multiplication: 1/2×1/10=1/20.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.