Question

The US Forest Service requires a report of deer population in US National Parks. Teams use a method called "Capture-Recapture" to estimate wildlife populations. To estimate the population over a wide area, samples are taken in which a number of deer are captured, tagged, and released back into the environment to mingle with the rest of the herd. Later, a larger sample of deer are captured, some of which are tagged and some are not. Parks officials use the ratio of tagged to untagged deer in the sample to project the population for the entire herd. Nick and his team initially collected, tagged, and released 24 deer. Several days later, the teams returned to the area and captured 55 deer, of which 9 were tagged. Find the estimated number of deer in this population (to the nearest whole number) if we presume that this sample ratio is typical for the entire herd.

Answer 1

Answer:

Step-by-step explanation:

Taking the ratio of numbers of deers tagged to the total numbers of deers, for 2 sample sizes, we have..

In the wide area, let the total number of deers be x, and the number of deers tagged is given to be 24.

In the sample, the total number of deers is given to be 48, and the number of tagged deers is given to be 13.

Equating the ratio of number of tagged deers to the total number of deers on both sides, we have

24/x = 13/48

Therefore,

x = 24*48/13 = 88.61 which is nearly equals to 89 deers.