NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
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Population investigations

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A school in Melbourne wants to estimate the average daily electricity consumption (in kWh) for households in the city. They randomly select 50 households from a list of 10,000 households and record their daily consumption over one week.

The total electricity consumption for the 50 households is 12,500 kWh.

What is the exact average daily electricity consumption per household in the sample?

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Explanation

Worked solution and answer (click to reveal)

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Worked solution

  1. The total electricity consumption for the 50 households over one week is given as 12,500 kWh.
  2. To find the average daily consumption per household, first determine the total daily consumption for the sample by dividing the weekly total by 7 days.
  3. Substitute the values: total daily consumption = 12,500 kWh ÷ 7 days.
  4. Perform the division: 12,500 ÷ 7 = 1,785.714285... kWh per day for the 50 households.
  5. Now divide this daily total by the number of households (50) to find the average daily consumption per household.
  6. Substitute: average daily consumption = 1,785.714285... kWh ÷ 50 households.
  7. Perform the division: 1,785.714285... ÷ 50 = 35.7142857... kWh per household per day.
  8. Express the result as a fraction to maintain exactness. 12,500 ÷ 7 ÷ 50 = 12,500 ÷ (7 × 50) = 12,500 ÷ 350.
  9. Simplify 12,500 ÷ 350. First divide numerator and denominator by 10: 1,250 ÷ 35.
  10. Simplify 1,250 ÷ 35. Divide both by 5: 250 ÷ 7.
  11. 250 ÷ 7 = 35 and 5/7, which is 35.714285... kWh. This is the exact average daily consumption per household.
  12. The exact average daily electricity consumption per household in the sample is 250/7 kWh, which is approximately 35.71 kWh. The question asks for the exact value.

Reference answer: 250/7

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