Credit Data, Inc., 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 he or she initiates contact, informs a consumer about an outstanding debt, discusses a payment plan, and receives payments by phone. Credit Data is mostly interested in how quickly a collector can initiate and end a conversation to move on to the next call. For employees of Credit Data, time is money in the sense that one account may require one call and 3 minutes to collect, whereas another account may take five calls and 11 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 9 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 11.5 minutes. Required Tasks: (A) 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 10% requirement. (B) Assuming that the standard deviation can be affected by training but the mean time will remain at 9 minutes, to what level must the standard deviation be reduced in order to meet the 10% requirement? (C) If nothing is done, what percent of all calls can be expected to require more than 11.5 minutes?
Credit Data, Inc., 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 he or she initiates contact, informs a consumer about an outstanding debt, discusses a payment plan, and receives payments by phone. Credit Data is mostly interested in how quickly a collector can initiate and end a conversation to move on to the next call. For employees of Credit Data, time is money in the sense that one account may require one call and 3 minutes to collect, whereas another account may take five calls and 11 minutes per call to collect. The company has discovered that the time collectors spend talking to consumers about accounts is approximated by a
Required Tasks:
(A) 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 10% requirement.
(B) Assuming that the standard deviation can be affected by training but the mean time will remain at 9 minutes, to what level must the standard deviation be reduced in order to meet the 10% requirement?
(C) If nothing is done, what percent of all calls can be expected to require more than 11.5 minutes?
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