Thirty-three small communities in Connecticut (population near10,000 each) gave an average of x = 138.5 reported cases of larcenyper year. Assume that σ is known to be 43.7 cases per year. (a)Find a 90% confidence interval for the population mean annualnumber of reported larceny cases in such communities. What is themargin of error? (Round your answers to one decimal place.) lowerlimit upper limit margin of error (b) Find a 95% confidenceinterval for the population mean annual number of reported larcenycases in such communities. What is the margin of error? (Round youranswers to one decimal place.) lower limit upper limit margin oferror (c) Find a 99% confidence interval for the population meanannual number of reported larceny cases in such communities. Whatis the margin of error? (Round your answers to one decimal place.)lower limit upper limit margin of error (d) Compare the margins oferror for parts (a) through (c). As the confidence levels increase,do the margins of error increase? As the confidence levelincreases, the margin of error remains the same. As the confidencelevel increases, the margin of error decreases. As the confidencelevel increases, the margin of error increases. (e) Compare thelengths of the confidence intervals for parts (a) through (c). Asthe confidence levels increase, do the confidence intervalsincrease in length? As the confidence level increases, theconfidence interval decreases in length. As the confidence levelincreases, the confidence interval remains the same length. As theconfidence level increases, the confidence interval increases inlength.