A park keeper wants to estimate the number of fish in a lake.
She catches 30 fish, tags them and puts them back in the lake.
The next day she catches 40 fish. 8 of these fish are tagged.
Work out an estimate for the number of fish in the lake.
2 marks
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150
2
An ecologist wants to estimate the number of blackbirds in a wood.
She catches 25 blackbirds, puts a ring on each one and releases them.
A week later she catches 60 blackbirds. 5 of them have rings.
Work out an estimate for the number of blackbirds in the wood.
State one assumption you made in working out your estimate.
3 marks
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a) 300b) Any one of: the population is unchanged between visits; the ringed birds mix fully with the population; rings are not lost; each bird is equally likely to be caught
3
A gardener wants to estimate the number of snails in her garden.
One evening she collects 45 snails, marks each shell with a dot of paint and releases them.
Two evenings later she collects 36 snails. 9 of them are marked.
Work out an estimate for the number of snails in the garden.
Write down one assumption you have made.
3 marks
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a) 180b) Any one of: marked snails mix evenly; no marks wash off; population unchanged; every snail equally likely to be collected
4
A scientist wants to estimate the number of beetles in a field.
He captures 50 beetles, marks them and releases them.
Later he captures 48 beetles. 6 of them are marked.
Work out an estimate for the number of beetles in the field.
Some of the paint marks rubbed off before the second capture. Explain how this affects your estimate.
3 marks
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a) 400b) The estimate is an overestimate - marked beetles are undercounted, so dividing by a smaller number makes the estimate too large
5
A warden wants to estimate the number of rabbits in a nature reserve.
She traps 60 rabbits, tags them and releases them.
The following week she traps 45 rabbits. 9 of them are tagged.
Work out an estimate for the number of rabbits in the reserve.
State one assumption needed for your estimate to be valid.
The warden set her second traps close to where she released the tagged rabbits. Explain what effect this could have on your estimate.
4 marks
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a) 300b) Any one of: tagged rabbits mix fully; population unchanged; tags not lost; all rabbits equally likely to be trappedc) Too many tagged rabbits would be recaptured, making the tagged proportion too high, so the estimate would be an underestimate
6
A ranger wants to estimate the number of deer in a forest.
He catches 80 deer, fits each one with an ear tag and releases them.
A month later he observes 120 deer. 15 of them have ear tags.
Work out an estimate for the number of deer in the forest.
The ranger believes the forest holds at least 800 deer. Does your estimate support his belief? Give a reason.
State one assumption your estimate relies on.
4 marks
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a) 640b) No; 640 < 800 so the estimate does not support at least 800 deerc) Any one of: tagged deer mix fully; population unchanged over the month; tags not lost; every deer equally likely to be observed
7
Using a capture-recapture study, the number of carp in a reservoir was estimated to be 600. In that study, 72 carp were tagged.
A new sample of 50 carp is caught. Work out how many of these carp you would expect to be tagged.
In fact, 10 of the 50 carp in the new sample are tagged. What does this suggest about the number of carp in the reservoir? Show your working.
4 marks
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a) 6b) New estimate = 360, so the population is likely to be smaller than 600
8
A marine biologist wants to estimate the number of crabs on a stretch of shore.
She collects 150 crabs, marks their shells and returns them to the shore.
The next day she collects a sample of 200 crabs. 12% of the crabs in this sample are marked.
Work out an estimate for the number of crabs on the shore.
State two assumptions your estimate relies on.
4 marks
Show answer
a) 1250b) Two of: full mixing; unchanged population; no lost marks; equal chance of capture
Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.