Calls to a customer service center last on average 1.4 minutes with a standard d

Question

Calls to a customer service center last on average 1.4 minutes with a standard deviation of 1.7 minutes. An operator in the call center is required to answer 52 calls each day. Assume the call times are independent. What is the expected total amount of time in minutes the operator will spend on the calls each day? Give an exact answer. 72.8 What is the standard deviation of the total amount of time in minutes the operator will spend on the calls each day? Give your answer to four decimal places. 12.2588 What is the approximate probability that the total time spent on the calls will be greater than 74 minutes? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question. What is the value c such that the approximate probability that the total time spent on the calls each day is less than c is 0.9? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question.

Explanation / Answer

1) total expected time =52*1.4=72.8

2) std deviation =1.7*(52)1/2 =12.2589

3)P(X>74)=1-P(X<74)=1-P(Z<(74-72.8)/12.2589)=1-P(Z<0.0979)=1-0.539=0.4610

4)for 90 percentile z=1.2816

hence corresponding c =72.8+1.2816*12.2589=88.5104

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