Question
Of the 50 fish that Alan caught from the lake, 14 were trout. The estimated population of the lake is 7,500 fish. About how many trout would you expect to be in the lake?
Ask by Owen Harris. in the United States
Feb 05,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
You would expect about 2,100 trout in the lake.
Solution
To estimate the number of trout in the lake, you can use a proportion based on the sample Alan caught.
**Given:**
- Alan caught **50 fish**, and **14** of them were trout.
- The **estimated total population** of the lake is **7,500 fish**.
**Steps to Estimate the Number of Trout:**
1. **Determine the proportion of trout in Alan's sample:**
\[
\frac{\text{Number of Trout}}{\text{Total Fishes Caught}} = \frac{14}{50}
\]
2. **Set up the proportion to find the estimated number of trout in the entire lake:**
\[
\frac{14}{50} = \frac{x}{7,500}
\]
Here, \( x \) represents the estimated number of trout in the lake.
3. **Solve for \( x \):**
\[
x = \frac{14 \times 7,500}{50} = \frac{105,000}{50} = 2,100
\]
**Conclusion:**
Based on the sample, you would expect there to be approximately **2,100 trout** in the lake.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To estimate the number of trout in the lake, you can use proportions. Since Alan caught 14 trout out of 50 fish, that gives you a ratio of 14/50. To find the expected number of trout in the entire population of 7,500 fish, you can set up the equation: (14/50) = (x/7500), where x is the expected number of trout. Cross-multiplying and solving gives x = (14 * 7500) / 50, which equals 2,100 trout in the lake. So, the expected number of trout in the lake is about 2,100! Happy fishing!
