Suppose Forty Communities Have an Average of Reported Cases of Larceny

Suppose forty communities have an average of reported cases of larceny per year. Assume that $\sigma$ is known to be 39.7 cases per year. Find an 85%, 90%, and 98% confidence interval for the population mean annual number of reported larceny cases in such communities. Compare the margins of error. As the confidence level increase, do the margins of error increase? $$\bar { x } = 134.7$$

A) The 85% confidence level has a margin of error of 57.2; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 92.5. As the confidence level increases, the margins of error increase.
B) The 85% confidence level has a margin of error of 9.0; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 14.6. As the confidence level increases, the margins of error increase.
C) The 85% confidence level has a margin of error of 1.4; the 90% confidence level has a margin of error of 1.6; and the 98% confidence level has a margin of error of 2.3. As the confidence level increases, the margins of error increase.
D) The 85% confidence level has a margin of error of 14.6; the 90% confidence level has a margin of error of 10.3; and the 98% confidence level has a margin of error of 9.0. As the confidence level increases, the margins of error decrease.
E) The 85% confidence level has a margin of error of 92.5; the 90% confidence level has a margin of error of 65.3; and the 98% confidence level has a margin of error of 57.2. As the confidence level increases, the margins of error decrease.