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.

1.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.

2.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. The standard deviation of the total amount of time in minutes the operator will spend on the calls each day is 52*1.7 = 88.4

2. Mean 52*1.4 = 72.8

On the normal probability tables , P( z < 1.282) = 0.90
z= (x-mean)/sd
1.282 = (x-72.8)/88.4
x=1.282*88.4 + 72.8
x=186.1288
or c=186.1288

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