Question

A Park ranger tags 100 animals. Use a proportion to estimate the total population for each sample.

Answer 1

Answer:

It is given that A Park ranger tags 100 animals.

This means the proportion of animals tagged= $\dfrac{100}{x}$

where 'x' represents the total population of animals.

We have to find total number of animals in each parts.

1)

23 out of 100 animals are tagged.

That means the proportion of animals tagged= $\dfrac{23}{100}$

Now we know that the proportion must be equal.

 $\dfrac{23}{100}=\dfrac{100}{x}$

⇒ $x=\dfrac{100\times 100}{23}=434.783$

which is approximately equal to 435.

Hence, the total population =435.

3)

8 out of 116 animals are tagged

That means the proportion of animals tagged= $\dfrac{8}{116}$

Now we know that the proportion must be equal.

 $\dfrac{8}{116}=\dfrac{100}{x}$

$x=\dfrac{100\times 116}{8}\\\\x=\dfrac{11600}{8}=1450$

which is approximately equal to 1450

Hence, the total population =1450.

4)

5 out of 63 animals are tagged

That means the proportion of animals tagged= $\dfrac{5}{63}$

Now we know that the proportion must be equal.

 $\dfrac{5}{63}=\dfrac{100}{x}$

$x=1260$

Hence, the total population =1260.

5)

4 out of 83 animals are tagged

That means the proportion of animals tagged= $\dfrac{4}{83}$

Now we know that the proportion must be equal.

 $\dfrac{4}{83}=\dfrac{100}{x}$

$x=\dfrac{100\times 83}{4}\\\\x=2075$

Hence, the total population =2075.

6)

3 out 121 animals are tagged

That means the proportion of animals tagged= $\dfrac{3}{121}$

Now we know that the proportion must be equal.

 $\dfrac{3}{121}=\dfrac{100}{x}$

$x=\dfrac{100\times 121}{3}\\\\x=4033.33$

Hence, the total population =4033.

7)

83 out of 125 animals are tagged

That means the proportion of animals tagged= $\dfrac{83}{125}$

Now we know that the proportion must be equal.

 $\dfrac{83}{125}=\dfrac{100}{x}$

$x=\dfrac{100\times 125}{83}\\\\x=150.6024$

Hence, the total population =151.

8)

7 out 165 animals are tagged

That means the proportion of animals tagged= $\dfrac{7}{165}$

Now we know that the proportion must be equal.

 $\dfrac{7}{165}=\dfrac{100}{x}$

$x=\dfrac{100\times 165}{7}\\\\x=2357.143$

Hence, the total population =2357.