Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting times in table 1.8 is x ~ = 5.46. If we let μ denote the mean of all possible bank customer waiting times using the new system and assume that σ equals 2.47:
a. calculate 95% and 99% confidence intervals for μ
b. using the 95% confidence interval, can the bank manager be 95% confident that μ is less than 6 minutes? Explain
c. Using the 99% confidence interval, can the bank manager be 99% confident that μ is less than 6 minutes? Explain
d. Based on your answers to parts b and c how convinced are you the the new mean waiting time is less than six minutes?