Question

Difficulty: MediumStatistical Sampling and Studies

A marine biologist wants to estimate the number of blue crabs in a bay that are infected with a specific parasite. The biologist captures a random sample of 250250 blue crabs from the bay, finds that 1515 of the crabs are infected, and then releases them. Based on this sample, if there is a total population of 12,00012,000 blue crabs in the bay, what is the best estimate of the total number of blue crabs infected with the parasite?

Answer: 720

Answer

The best estimate of the total number of blue crabs infected with the parasite is 720.
The correct answer is found by establishing the sample proportion of infected crabs, which is 15 out of 250, or 6%. Multiplying this rate by the total estimated population of 12,000 crabs yields 720.

Step-by-Step Solution

1
Calculate the proportion of infected crabs in the sample.
15250=0.06\frac{15}{250} = 0.06
To determine the rate of infection in the representative sample.
2
Multiply the sample proportion by the total population of blue crabs in the bay.
0.06×12,000=7200.06 \times 12,000 = 720
To generalize the sample rate to the entire population of crabs in the bay.

Key Concept

Generalizing a sample proportion to estimate a population parameter.
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