NavGanitMateby NavGreen Compute, AustraliaBased on Australian Curriculum: Mathematics v9.0
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Evaluating statistical claims

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A statistical report in Melbourne claims that 55% of people aged 18–35 in the city have used a digital fitness tracker in the past year. The report is based on a survey of 1600 randomly selected individuals from this age group.

The survey found that 880 people had used a digital fitness tracker.

What is the exact proportion of respondents who used a digital fitness tracker, expressed as a simplified fraction?

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Worked solution

  1. The survey included 1600 individuals aged 18–35 in Melbourne.
  2. Of these, 880 reported having used a digital fitness tracker in the past year.
  3. To find the proportion, divide the number of users by the total number surveyed: 880 ÷ 1600.
  4. Write the fraction: 880 / 1600.
  5. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD).
  6. Find the GCD of 880 and 1600 using prime factorisation: 880 = 2^4 × 5 × 11, 1600 = 2^6 × 5^2.
  7. The common prime factors are 2^4 and 5, so GCD = 2^4 × 5 = 16 × 5 = 80.
  8. Divide numerator and denominator by 80: 880 ÷ 80 = 11, 1600 ÷ 80 = 20.
  9. The simplified fraction is 11/20.
  10. Check: 11 ÷ 20 = 0.55, and 0.55 × 1600 = 880, which matches the original data.
  11. The exact proportion of respondents who used a digital fitness tracker is 11/20.
  12. This matches the claim of 55% (since 55% = 55/100 = 11/20), confirming accuracy.

Reference answer: 11/20

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