Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
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.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
