To gather information about the elk population, biologist marked 75 elk. Later, they flew over the region and counted 250 elk, of which 15 were marked. What is the best estimate for the elk population?
To estimate the elk population, we can use the concept of population proportion.
1. Calculate the proportion of marked elk in the sample:
Proportion of marked elk = Number of marked elk / Total number of counted elk
= 15 / 250
= 0.06
2. Use the proportion of marked elk to estimate the elk population:
Estimated elk population = Number of marked elk / Proportion of marked elk
= 75 / 0.06
= 1250
Therefore, the best estimate for the elk population is 1250.
To estimate the elk population, we can use a method called the Lincoln-Petersen Index. The formula for this index is:
N = (M * S) / R
Where:
N = Total population size
M = Number of individuals marked in the first sample
S = Total number of individuals in the second sample
R = Number of individuals in the second sample that are marked
In this case, M = 75 (number of marked elk), S = 250 (total number of elk counted in the second sample), and R = 15 (number of marked elk observed in the second sample).
Plugging these values into the formula:
N = (75 * 250) / 15
N = 1250
The best estimate for the elk population is 1250 individuals.
One way to approach this problem is to use a proportion:
(markeds in sample) / (total in sample) = (markeds in population) / (total population)
We can plug in the numbers we know:
15 / 250 = 75 / x
where x is the total elk population. We can cross-multiply and solve for x:
15x = 75 * 250
x = 18,750
Therefore, the best estimate for the elk population is 18,750.
A 1,250
B 1,300
C 1,200
D 1,350
these the only options they have..