Public Policy and Political Science
A building inspector enforces building, electrical, mechanical, plumbing, and energy code requirements for the safety and health of people in a certain city, county, or state. In Santa Cruz County, the probability that a building inspector will find at least one code violation at a commercial building is 0.25. Suppose 30 commercial buildings are selected at random.
a. Find the mean, variance, and standard deviation of the number of commercial buildings with at least one violation.
b. Find the probability that the number of commercial buildings with at least one violation will be within one standard deviation of the mean.
c. Find the probability that the number of commercial buildings with at least one violation will be more than two standard deviations from the mean.
d. Suppose the actual number of commercial buildings with at least one violation is 10. Is there any evidence to suggest that code violations are found in more than 25% of commercial buildings? Justify your answer.