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18 Apr 2018, 18:26
Kudos
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B
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Difficulty:
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Question Stats:
71% (01:56) correct
29%
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To estimate the population of horned lizards in a national park, a team from the park service captures and tags 25 horned lizards and then releases the tagged lizards back into the park. Two weeks later, the team returns and captures 20 horned lizards, 4 of which bear tags that identify them as being among the previously captured lizards. If all the tagged lizards have dispersed throughout the park an are still active when the second group of lizards is captured, what is the best estimate of the horned lizard population in the park, based on the information obtained through this capture-tagr-ecapture strategy?
(A) 250
(B) 125
(C) 100
(D) 80
(E) 75
(A) 250
(B) 125
(C) 100
(D) 80
(E) 75
18 Apr 2018, 20:02
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I just want to give it a try.
1. Total Tagged horned lizard = 25
2. Two weeks after team captures 20 lizards, of which 4 lizards are already tagged (from previously captured lizards)
=> \(\frac{{Untagged Horned Lizard}}{{tagged Horned Lizard}}\) = \(\frac{16}{4}\) = \(\frac{4}{1}\)
=> Total Untagged Horned Lizard = \(\frac{4}{1}\)* Total Tagged horned lizard
= \(\frac{4}{1} * 25\)
= 100
Hence Total Horned Lizard = Tagged Lizard + Untagged Lizard = 25 + 100 = 125
1. Total Tagged horned lizard = 25
2. Two weeks after team captures 20 lizards, of which 4 lizards are already tagged (from previously captured lizards)
=> \(\frac{{Untagged Horned Lizard}}{{tagged Horned Lizard}}\) = \(\frac{16}{4}\) = \(\frac{4}{1}\)
=> Total Untagged Horned Lizard = \(\frac{4}{1}\)* Total Tagged horned lizard
= \(\frac{4}{1} * 25\)
= 100
Hence Total Horned Lizard = Tagged Lizard + Untagged Lizard = 25 + 100 = 125
19 Apr 2018, 15:57
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Bunuel
Of 20 lizards caught the second time, 4 are tagged, which constitutes
\(\frac{4}{20}=.20*100=20\) percent of the lizards caught
That's a sample of the whole lizard population.
The total number of tagged lizards, now dispersed, should be represented in the whole population in the same percent, roughly, as the percent of tagged lizards sample (the second catch.)
25 tagged lizards = .20 of all lizards
All lizards = \(\frac{25}{.2}= 125\) lizards
Answer B
