The safety inspector in a large city wants to estimate the proportion of buildings in the city that are in violation of fire codes. A random sample of 35 buildings is chosen for inspection, and 3 of them are found to have fire code violations. Estimate the proportion of buildings in the city that have fire code violations, and find the uncertainty in the estimate.

Check Explanation.

Step-by-step explanation:

The sample will be a representative of the entire build us in the city.

For a sample size 35, 3 have fire code violations, hence, the proportion of houses with fire code violations = (3/35) = 0.0857 = 8.57 %

The uncertainty in the estimate is given in the form of standard error.

Standard error = √[ (p (1-p) / n]

n = sample size = 35, p = 0.0857, 1 - p = 0.9143

Standard error of the sample = √ (0.0857*0.9143/35) = 0.1616

In terms of the population, (0.1616/35) = 0.00462

Proportion of buildings with fire code violations = (8.57 ± 0.462) %