To answer the given questions accurately and in detail, let's break down each question step-by-step based on the provided data:
\begin{tabular}{|c|c|c|}
\hline
Length (inches) & Weight (ounces) & Category \\
\hline
3 & 3 & Juvenile \\
\hline
4 & 5 & Adult \\
\hline
5 & 8 & Adult \\
\hline
6 & 2 & Juvenile \\
\hline
7 & 10 & Adult \\
\hline
8 & 9 & Juvenile \\
\hline
9 & 4 & Juvenile \\
\hline
10 & 4 & Juvenile \\
\hline
\end{tabular}
### 1. Percentage of sample that were juveniles over 8 inches long
First, let's count the total number of fish. There are 8 fish in the sample.
Next, count the number of juvenile fish:
- Juveniles: (3, 3), (6, 2), (8, 9), (9, 4), (10, 4) → 5 juveniles
Now, count the number of juveniles over 8 inches long:
- Over 8 inches: (9, 4), (10, 4) → 2 juveniles
Therefore, the percentage of juveniles over 8 inches long is:
[tex]\[
\frac{2}{8} \times 100 = 25\%
\][/tex]
### 2. Mean length of all fish in the sample
Sum the lengths of all the fish:
[tex]\[
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 52 \text{ inches}
\][/tex]
Divide by the number of fish:
[tex]\[
\frac{52}{8} = 6.5 \text{ inches}
\][/tex]
### 3. Percentage of sample that were adult fish
Count the number of adult fish:
- Adults: (4, 5), (5, 8), (7, 10) → 3 adults
Therefore, the percentage of adult fish is:
[tex]\[
\frac{3}{8} \times 100 = 37.5\%
\][/tex]
### 4. Mean length of juvenile fish in the sample
Sum the lengths of juvenile fish:
[tex]\[
3 + 6 + 8 + 9 + 10 = 36 \text{ inches}
\][/tex]
Divide by the number of juvenile fish:
[tex]\[
\frac{36}{5} = 7.2 \text{ inches}
\][/tex]
### 5. Mean length of adult fish in the sample
Sum the lengths of adult fish:
[tex]\[
4 + 5 + 7 = 16 \text{ inches}
\][/tex]
Divide by the number of adult fish:
[tex]\[
\frac{16}{3} \approx 5.33 \text{ inches}
\][/tex]
### 6. Percentage of sample that were juvenile fish
Therefore, the percentage of juvenile fish is:
[tex]\[
\frac{5}{8} \times 100 = 62.5\%
\][/tex]
### Summary:
1. Percentage of sample that were juveniles over 8 inches long: 25\%
2. Mean length of all fish in the sample: 6.5 inches
3. Percentage of sample that were adult fish: 37.5\%
4. Mean length of juvenile fish in the sample: 7.2 inches
5. Mean length of adult fish in the sample: 5.33 inches
6. Percentage of sample that were juvenile fish: 62.5\%
Note: Correcting the inconsistent values provided in the question text. The detailed calculations provide accurate metrics.
