Using six random samples, the average number of catfish in the samples was 5.7. If the total population of fish in the pond is 200, the proportion of catfish in the pond will be [tex]$\frac{5.7}{20}=\frac{x}{200}$[/tex]
What is the predicted number of catfish in the pond?
Answer (2)
Set up the proportion equation: 6 5.7 = 200 x .
Multiply both sides by 200 to isolate x: x = 6 5.7 × 200 .
Calculate the value of x: x = 190 .
The predicted number of catfish in the pond is 190 .
Explanation
Understanding the Problem We are given that the average number of catfish in six random samples is 5.7. The total population of fish in the pond is 200. We are also given the proportion equation 6 5.7 = 200 x , where x represents the predicted number of catfish in the pond.
Setting up the Equation To find the predicted number of catfish, we need to solve the proportion equation for x. The equation is: 6 5.7 = 200 x
Isolating x To solve for x, we multiply both sides of the equation by 200: x = 6 5.7 × 200
Calculating x Now, we perform the calculation: x = 6 5.7 × 200 = 6 1140 = 190
Final Answer Therefore, the predicted number of catfish in the pond is 190.
Examples
Imagine you are a marine biologist studying a pond's ecosystem. Using sample data, you can estimate the total number of a specific fish species in the pond. This method is valuable for managing fish populations, understanding ecological balance, and making informed decisions about conservation efforts. By understanding proportions, you can scale up your findings from a small sample to the entire population, providing crucial insights for effective environmental stewardship.
The predicted number of catfish in the pond is 190, calculated by setting up a proportion based on the average number found in samples. This involved isolating the variable in the proportion equation and solving for it. Using the calculated average from the samples allows us to estimate the total number of catfish in the entire pond population.
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