Question

writing a proportion
sample 1 2 3 4 5 6
catfish 3 5 7 5 6 8
all fish 20 20 20 20 20 20
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?
\\(\frac{5.7}{20} = \frac{x}{200}\\)
\\(\frac{5.7}{20} = \frac{200}{x}\\)
\\(\frac{34}{20} = \frac{x}{200}\\)
\\(\frac{8}{20} = \frac{20}{x}\\)

Explanation:

Step1: Identify sample ratio

The mean number of catfish per 20-fish sample is 5.7, so the sample ratio of catfish to total fish is $\frac{5.7}{20}$.

Step2: Set up population proportion

Let $x$ = total catfish in 200-fish pond. The population ratio is $\frac{x}{200}$. Equate sample and population ratios:
$\frac{5.7}{20} = \frac{x}{200}$

Answer:

$\boldsymbol{\frac{5.7}{20} = \frac{x}{200}}$ (first option)