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A survey was conducted in Sydney to estimate the proportion of residents who regularly use electric scooters for short commutes. The survey used a systematic sampling method, selecting every 15th household from a list of 12,000 households in the city.
The survey collected responses from 800 households. Of these, 240 reported regular electric scooter use.
What is the exact proportion of surveyed households that use electric scooters regularly? Express your answer as a simplified fraction.
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Worked solution
- The survey collected responses from 800 households in Sydney.
- Of these 800 households, 240 reported regular electric scooter use.
- To find the proportion of surveyed households that use electric scooters regularly, divide the number of households that use scooters by the total number surveyed.
- Set up the fraction: 240 / 800.
- Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (GCD).
- Find the GCD of 240 and 800. Both are divisible by 80: 240 ÷ 80 = 3, 800 ÷ 80 = 10.
- The simplified fraction is 3/10.
- Verify the simplification: 3/10 = 0.3, and 240 ÷ 800 = 0.3, so the result is correct.
- The proportion is exact and in simplest fractional form.
Reference answer: 3/10
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