Question

a sample of 50 fish in a pond revealed that 18 of them were greater than 16 inches in length. if there are an estimated 1100 fish in the pond, how many are expected to be 16 inches or smaller in length?

a) 320
b) 360
c) 396
d) 704

Explanation:

Step1: Calculate proportion of fish > 16 inches in sample

The proportion of fish greater than 16 inches in the sample of 50 fish is $\frac{18}{50}$.

Step2: Calculate expected number of fish > 16 inches in pond

If there are 1100 fish in the pond, the expected number of fish greater than 16 inches is $1100\times\frac{18}{50}=1100\times0.36 = 396$.

Step3: Calculate expected number of fish ≤ 16 inches in pond

The expected number of fish 16 inches or smaller is $1100 - 396=704$.

Answer:

D. 704