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30 March, 11:14

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.

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  1. 30 March, 13:13
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    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) %
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