Question: Suppose forty-five communities gave an average of \(\bar{X}\) = 122.5 reported cases of larceny per year. Assume that sigma is known to be 36.5 cases per year. Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities.

a) Calculate the margin of error (you may use excel or your calculator)

b) Now, calculate confidence interval

c) Write an interpretive sentence for the interval found above

d) Find the sample size necessary for a 95% confidence level with a maximum error of estimate E = 7 larcenies.