Suppose the top management of this chain of stores has decided that 90% of prescriptions should be filled in 13 minutes or less. The pharmacy department manager can accomplish this by changing either the mean or standard deviation of the distribution. Explain how this is possible. Then calculate A). the new mean (assuming the standard deviation remains at 2.5) and B). the new standard deviation (assuming the mean remains at 10) that would be required to achieve the management’s directive.

Suppose store # 4 has been receiving complaints about slow service. The manager of this store insists that these complaints are unfounded, and that the mean waiting time in her store is no more than 10 minutes – equivalent to the overall average for the entire chain of stores. The company has sent you to store # 4 to investigate. You question a random sample of 25 customers and find that in this sample, the average waiting time is 11 minutes. What is the probability of finding a sample mean of 11 minutes if the true mean is actually 10 minutes, as the manager claims? Based on this probability, what would you report to the company?