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Difficulty: MediumStatistical Sampling and Studies

A municipal utility department wants to estimate the number of residential water service lines that contain lead in a community with 3,6003,600 homes. The department selects a random sample of 120120 homes and inspects their water service lines. The inspection reveals that 99 of the sampled homes have lead service lines. Based on the results of this sample, what is the estimated number of homes in the entire community that have lead service lines?

Answer: 270

Answer

The estimated number of homes in the community that have lead service lines is 270.
Based on the random sample, the proportion of homes with lead service lines is 9 out of 120, which is 0.075 (or 7.5%). Generalizing this to the entire population of 3,600 homes yields an estimate of 0.075×3,600=2700.075 \times 3,600 = 270 homes.

Step-by-Step Solution

1
Calculate the proportion of homes in the sample with lead service lines.
9120=0.075\frac{9}{120} = 0.075
To find the sample proportion, divide the number of homes with lead service lines by the total number of homes inspected.
2
Estimate the total number of homes in the community with lead service lines.
0.075×3,600=2700.075 \times 3,600 = 270
Multiply the total number of homes in the community by the proportion found in the random sample.

Key Concept

Estimating population parameters and totals from a random sample.
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Topics

Statistical Sampling and Studies

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