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Sagot :
Let's work through the problem step by step, recording the data for each day and calculating the required estimates.
### Day 1
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
This is calculated as the number of tagged fish caught divided by the total number of fish caught.
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
Using the formula [tex]\(\text{Estimated Population} = \frac{\text{Initial Tagged Fish}}{\text{Probability}}\)[/tex],
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 1 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 1} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Day 2
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 2 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 2} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Day 3
1. Number of fish tagged out of 10 fish caught: 1
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{1}{10} = 0.1 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.1} = 1000 \][/tex]
So, the data for Day 3 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 3} & 1 & 0.1 & 1000 \\ \hline \end{array} \][/tex]
### Day 4
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 4 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 4} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Summary Table
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day} & \text{Number of tagged fish caught} & \text{Experimental probability} & \text{Estimated number of fish} \\ \hline \text{Day 1} & 8 & 0.8 & 125 \\ \hline \text{Day 2} & 8 & 0.8 & 125 \\ \hline \text{Day 3} & 1 & 0.1 & 1000 \\ \hline \text{Day 4} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Analysis of Estimated Populations
- Smallest estimated population: 125
- Largest estimated population: 1000
### Conclusion
Based on the data collected over 4 days, the population of fish in the pond is estimated to be between 125 and 1000.
My guess for the population of fish in the pond falls within this interval:
- Select the smallest number: 125
- Select the largest number: 1000
Finally, after checking the actual population size in the POND tab, we will know if our estimates and guesses were accurate.
### Day 1
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
This is calculated as the number of tagged fish caught divided by the total number of fish caught.
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
Using the formula [tex]\(\text{Estimated Population} = \frac{\text{Initial Tagged Fish}}{\text{Probability}}\)[/tex],
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 1 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 1} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Day 2
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 2 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 2} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Day 3
1. Number of fish tagged out of 10 fish caught: 1
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{1}{10} = 0.1 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.1} = 1000 \][/tex]
So, the data for Day 3 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 3} & 1 & 0.1 & 1000 \\ \hline \end{array} \][/tex]
### Day 4
1. Number of fish tagged out of 10 fish caught: 8
2. Experimental probability of catching a tagged fish:
[tex]\[ \text{Probability} = \frac{8}{10} = 0.8 \][/tex]
3. Estimated number of fish in the pond:
[tex]\[ \text{Estimated Population} = \frac{100}{0.8} = 125 \][/tex]
So, the data for Day 4 is:
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day 4} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Summary Table
[tex]\[ \begin{array}{|c|c|c|c|} \hline \text{Day} & \text{Number of tagged fish caught} & \text{Experimental probability} & \text{Estimated number of fish} \\ \hline \text{Day 1} & 8 & 0.8 & 125 \\ \hline \text{Day 2} & 8 & 0.8 & 125 \\ \hline \text{Day 3} & 1 & 0.1 & 1000 \\ \hline \text{Day 4} & 8 & 0.8 & 125 \\ \hline \end{array} \][/tex]
### Analysis of Estimated Populations
- Smallest estimated population: 125
- Largest estimated population: 1000
### Conclusion
Based on the data collected over 4 days, the population of fish in the pond is estimated to be between 125 and 1000.
My guess for the population of fish in the pond falls within this interval:
- Select the smallest number: 125
- Select the largest number: 1000
Finally, after checking the actual population size in the POND tab, we will know if our estimates and guesses were accurate.
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