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 40 buildings is chosen for inspection, and 4 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.

Proportion of buildings in the city that have fire code violations: 10%

Uncertainty 0.3 = 30%

Step-by-step explanation:

This situation complies with a binomial model where p is the probability of finding a building having fire code violations and q=1-p

Since in random sample of 40 buildings chosen for inspection 4 of them are found to have fire code violations, the proportion  is 4/40 = 0.1 or 10% and  p=0.1 as well.

In a binomial model the standard deviation s is:

where n is the sample size. So

and the uncertainty is the standard error SE

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.