) A student, for want of something better to do, decided to go fishing in the NCBS pond. She caught 50 mosquito fish, but rather than take them home for dinner (they were too small anyway) she decided to just mark them and return them to the pond. A week later she went fishing again. This time she caught 40 mosquito fish, of which 5 were marked. Based on these data, what is the estimated size of the mosquito fish population in the pond?

To estimate the size of the mosquito fish population in the pond, we can use a technique called the Lincoln-Petersen index. It's based on the assumption that the ratio of marked individuals to the total population in the first sample will be the same as the ratio in the second sample.

Let's break down the steps:

1. Calculate the proportion of marked fish in the first sample:
- Number of marked fish in the first sample = 50
- Total number of fish in the first sample = 50 (since all were marked)
- Proportion of marked fish in the first sample = Number of marked fish / Total number of fish = 50 / 50 = 1

2. Use the proportion from the first sample to estimate the total population size:
- Number of marked fish in the second sample = 5
- Total number of fish in the second sample = 40
- Estimated population size = Total number of fish in the second sample / Proportion of marked fish in the first sample = 40 / 1 = 40

Therefore, the estimated size of the mosquito fish population in the pond is 40.

To estimate the size of the mosquito fish population in the pond, we can use a method called the Lincoln-Petersen index. According to this method, we can make an assumption that the ratio of marked fish caught to the total number of fish in the first sample is equal to the ratio of marked fish caught to the total number of fish in the second sample.

Let's break down the information given:

First Sample:
- Number of fish caught: 50
- Number of marked fish: 50

Second Sample:
- Number of fish caught: 40
- Number of marked fish: 5

Using the Lincoln-Petersen index formula:
Estimated population size = (Number of fish caught in first sample * Number of fish caught in second sample) / Number of marked fish recaptured

Plugging in the given data:
Estimated population size = (50 * 40) / 5
Estimated population size = 200

The estimated size of the mosquito fish population in the pond is 200.

50 fish and all marked.

40 fish and 5 marks found. so you found 5 of 50 or 1/10. So you should have how many total fish in the pond as an estimate.