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Shirley wants to find an estimate for the number of bees in her hive - Edexcel - GCSE Maths - Question 17 - 2020 - Paper 1

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Shirley wants to find an estimate for the number of bees in her hive. On Monday she catches 90 of the bees. She puts a mark on each bee and returns them to her hive... show full transcript

Worked Solution & Example Answer:Shirley wants to find an estimate for the number of bees in her hive - Edexcel - GCSE Maths - Question 17 - 2020 - Paper 1

Step 1

Work out an estimate for the total number of bees in her hive.

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Answer

To estimate the total number of bees, we can use the formula:

extTotalBees=Total Captured on Tuesday×Total Marked on MondayMarked Count from Tuesday ext{Total Bees} = \frac{\text{Total Captured on Tuesday} \times \text{Total Marked on Monday}}{\text{Marked Count from Tuesday}}

  1. Capture data:

    • Monday: 90 marked bees
    • Tuesday: 120 total captured, with 20 marked bees

  2. Substitute the values into the formula:

    • Total Bees =120×9020= \frac{120 \times 90}{20}
    • Total Bees =1080020= \frac{10800}{20}
    • Total Bees =540= 540

Thus, the estimated total number of bees in her hive is 540.

Step 2

If Shirley's assumption is wrong, explain what effect this would have on your answer to part (a).

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Answer

If marks fall off Shirley, she will have over-estimated the number of bees in her hive. This is because if the marked bees are not appropriately recognized, it could lead to counting existing unmarked bees as newly marked, resulting in fewer actual bees overall. Consequently, her estimate would be too high, affecting the reliability of the estimate derived in part (a).

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