A debt collection company has been monitoring the amount of time its bill collectors spend on calls that produce contacts with consumers. Management is interested in the distribution of time a collector spends on each call in which they initiate contact, inform a consumer about an outstanding debt, discuss a payment plan, and receive payments by phone. The company mostly interested in how quickly a collector can initiate and end a conversation to move on to the next call. For employees of the company, time is money in the sense that one account may require one call and 2 minutes to collect, whereas another account may take five calls and 10 minutes per call to collect. The company has discovered that the time collectors spend talking to consumers about accounts is approximated by a normal distribution with a mean of 8 minutes and a standard deviation of 2.5 minutes. The managers believe that the mean is too high and should be reduced by more efficient phone call methods. Specifically, they wish to have no more than 10% of all calls require more than 10.5 minutes.
Which formulas are used to find the answers to the following:
1. Assuming that training can affect the average time but not the standard deviation, the managers are interested in knowing to what level the mean call time needs to be reduced in order to meet the 1 0% requirement.
2. Assuming that the standard deviation can be affected by training but the mean time will remain at 8 minutes, to what level must the standard deviation be reduced in order to meet the 10% requirement?
3. If nothing is done, what percent of all calls can be expected to require more than 10.5 minutes?