3. UIW developed an active-duty satisfaction survey that was released to about 1100 service members. Service members took an average of 9.5 minutes to complete the survey with a known standard deviation of 2.6 minutes. The population distribution is assumed to be normal.

Only answers that show full calculations will be graded (not optional)

a. a. Construct a 92% confidence interval for the population mean time to complete the survey. State the confidence interval, and calculate the error bound.

b. b. Let's suppose that UIW releases another survey. By keeping the same error-bound margin, but now surveying only 600 service members instead of 1100, what would happen to the level of confidence? Why?

c. c. Let's suppose that Dr. Evans, President of UIW, tells us that he wants to be 99% sure about the average time to complete the survey. Does UIW have to increase the number of service members surveyed? Why or why not?