Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers

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Recall that a bank manager has developed a new system to reducethe time customers spend waiting to be served by tellers duringpeak business hours. The mean waiting time during peak businesshours under the current system is roughly 9 to 10 minutes. The bankmanager hopes that the new system will have a mean waiting timethat is less than six minutes. The mean of the sample of 93 bankcustomer waiting times is x⎯⎯x¯ = 5.45. If welet µ denote the mean of all possible bankcustomer waiting times using the new system and assumethat σ equals 2.46:
(a) Calculate 95 percent and 99 percentconfidence intervals for µ. (Round youranswers to 3 decimal places.)
(b) Using the 95 percent confidenceinterval, can the bank manager be 95 percent confidentthat µ is less than six minutes? Explain.
(c) Using the 99 percent confidenceinterval, can the bank manager be 99 percent confidentthat µ is less than six minutes? Explain.
(d) Based on your answers toparts b and c, how convinced areyou that the new mean waiting time is less than six minutes?