Question

the mean number of catfish in all 6 samples is approximately 5.7. if 200 fish are in the pond, which proportion can be used to predict the number of catfish in the population?
o $\frac{5.7}{20}=\frac{x}{200}$
o $\frac{5.7}{20}=\frac{200}{x}$
o $\frac{34}{20}=\frac{x}{200}$
o $\frac{8}{20}=\frac{20}{x}$

Explanation:

Step1: Identify the proportion concept

We use the ratio of catfish to total - fish in the sample to predict the number in the population. The mean number of catfish per sample of 20 fish is 5.7. Let \(x\) be the number of catfish in the population of 200 fish.

Step2: Set up the proportion

The proportion is based on the fact that the ratio of catfish to total fish in the sample should be the same as the ratio in the population. So, \(\frac{\text{Mean number of catfish in sample}}{\text{Number of fish in sample}}=\frac{\text{Number of catfish in population}}{\text{Total number of fish in population}}\), which gives \(\frac{5.7}{20}=\frac{x}{200}\).

Answer:

A. \(\frac{5.7}{20}=\frac{x}{200}\)