If you could please help me with the following question. Thank you

12. [-l11 Points] BBRIEFSTAT58.1.016. I MYNOTES ll PRACTICEANOTHER I Consider college officials in admissions, registration, counseling, financial aid, campus ministry, food services, and so on. How much money do these people make each year? Suppose you read In your local newspaper that 46 officials In student services earned an average ofx = $50,340 each year. (a) Assume that a = $17,400 for sa aries of college officials in student services. Find a 90% confidence interval for the population mean salaries of such personnel. What is the margin of error? (Round your answers to the nearest whole number.) lower limit $ upper limit $ margin of error $ (b) Assume that a = $10,920 for sa arles of college officials In student services. Find a 90% confidence Interval for the population mean salaries of such personnel. What Is the margin of error? (Round your answers to the nearest whole number.) lower limit $ upper limit $ margin of error $ (c) Assume that a = $5,240 for salaries of college officials in student services. Find a 90% confidence inten/al for the population mean salaries of such personnel. What is the margin of error? (Round your answers to the nearest whole number.) lower limit $ upper limit $ margin of error $ (d) Compare the margins of error for parts (a) through (c). As the standard deviation decreases, does the margin of error decrease? 0 As the standard deviation decreases, the margin of error remains the same. 0 As the standard deviation decreases, the margin of error Increases. 0 As the standard deviation decreases, the margin of error decreases. (e) Compare the lengths of the confidence Inten/als for parts (a) through (c). As the standard deviation decreases, does the length of a 90% confidence interval decrease? 0 As the standard deviation decreases, the confidence interval increases in length. 0 As the standard deviation decreases, the confidence Interval decreases In length. 0 As the standard deviation decreases, the confidence Interval remains the same length