Question

1. a scientist caught 50 fish, marked them, and released them. later, they caught a random sample of 100 fish from the same area, and 5 of them were marked. which number below is the best estimate for the total fish population?

a. 500
b. 1,000
c. 2,000
d. 5,000

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked fish in the first catch to total population should equal the proportion of marked fish in the second catch to the second sample size. So, \(\frac{50}{N}=\frac{5}{100}\).

Step2: Solve for \( N \)

Cross - multiply: \( 5\times N = 50\times100 \). Then \( 5N=5000 \). Divide both sides by 5: \( N=\frac{5000}{5}=1000 \).

Answer:

b. 1,000