NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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In a study conducted in Sydney, researchers are estimating the proportion of residents who regularly use a local park for exercise. Two random samples are taken from the same population.

Sample 1 consists of 40 residents, and 18 of them report regular park use. Sample 2 consists of 160 residents, and 64 of them report regular park use.

What is the exact proportion of residents who report regular park use in Sample 2?

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Worked solution

  1. The question asks for the exact proportion of residents who report regular park use in Sample 2. The sample size is 160 residents, and 64 reported regular park use.
  2. The proportion is calculated as the number of residents who use the park regularly divided by the total number of residents in the sample.
  3. Substitute the given values into the proportion formula: proportion = 64 / 160.
  4. Simplify the fraction 64/160 by dividing both numerator and denominator by their greatest common divisor. First, divide both by 16: 64 ÷ 16 = 4, 160 ÷ 16 = 10.
  5. The simplified fraction is 4/10.
  6. Simplify 4/10 by dividing both numerator and denominator by 2: 4 ÷ 2 = 2, 10 ÷ 2 = 5.
  7. The fully simplified fraction is 2/5.
  8. The proportion 2/5 is equivalent to 0.4, but the question asks for the exact proportion, so the answer must be in fraction form.
  9. Verify the calculation: 2/5 = 0.4, and 0.4 × 160 = 64, which matches the number of residents who reported regular park use.
  10. The proportion is exact and does not require decimal approximation.
  11. The exact proportion of residents who report regular park use in Sample 2 is 2/5.
  12. The final answer is confirmed as 2/5, which is the exact proportion.

Reference answer: 2/5

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