Respuesta :
Answer:
540
Step-by-step explanation:
Let the estimate total population=y
Initially, out of a total of y, 54 are marked.
Then out of a sample of 290 cockatoos, 29 of them are marked.
We take the ratio of the population to the sample and do same for the number of marked in each category.
y:290 = 54: 29
[TeX]\frac{y}{290}=\frac{54}{29}[/TeX]
Cross multiplying
y X 29 = 290 X 54
Divide both sides by 29 to obtain y.
[TeX]\frac{y X 29}{29}=\frac{290 X 54}{29}[/TeX]
y= 54 X 10 =540
The best estimate of the cuckatoo population is 540
Answer:
the population size is 540 cockatoos
Step-by-step explanation:
Denoting P as the total population , since the person took the 54 cockatoos and mark them , after he released them there are a proportion of marked cockatoos in the population equal to
proportion of marked cockatoos = marked cockatoos / total number of cockatoos = 54 / P
then if he takes a sample , if we assume that the marked cockatoos are well mixed around the population and each cockatoo has the same probability of being trapped , then if we take cockatoos at random , is almost likely that he traps cockatoos in the same proportion , then
proportion of marked cockatoos = 29/290 = 54/P
P= 54 * 290 / 29 = 540 cockatoos
Note
- Mathematically , is the same that saying that each sample has the the same probability of being chosen.
- Actually if the traps 290 cockatoos out of 540 , the actual probability can be calculated through an hypergeometric distribution whose most probable value of the population size is 540 cockatoos
