Math Problem Statement

total marked fish: 19 total fish counted: 86 Total marked fish counted: 17 what is the best estimate for the population of fish? Answer to the closest whole number

Solution

To estimate the fish population using the mark-and-recapture method, you can use the following formula:

Estimated Population=Total Fish Counted×Total Marked FishMarked Fish Counted\text{Estimated Population} = \frac{\text{Total Fish Counted} \times \text{Total Marked Fish}}{\text{Marked Fish Counted}}

Plugging in the values given:

Estimated Population=86×1917\text{Estimated Population} = \frac{86 \times 19}{17}

Calculating this:

Estimated Population=16341796.12\text{Estimated Population} = \frac{1634}{17} \approx 96.12

Rounding to the closest whole number, the estimated population of fish is 96.

Would you like a detailed explanation of the method or have any other questions?

Here are five related questions:

  1. How does the mark-and-recapture method help in estimating wildlife populations?
  2. What are some factors that could affect the accuracy of a mark-and-recapture estimate?
  3. How might the estimate change if the number of marked fish counted was higher?
  4. What are other methods used in population estimation?
  5. How can you ensure that the marked sample is representative of the population?

Tip: Mark-and-recapture works best when the marked sample mixes evenly back into the population.

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Math Problem Analysis

Mathematical Concepts

Statistics
Estimation
Mark-and-Recapture Method

Formulas

Estimated Population = (Total Fish Counted * Total Marked Fish) / Marked Fish Counted

Theorems

Mark-and-Recapture Estimation

Suitable Grade Level

Grades 9-11