Calls to a customer service center last on average 1.7 minutes with a standard d

Question

Calls to a customer service center last on average 1.7 minutes with a standard deviation of 1.2 minutes. An operator in the call center is required to answer 82 calls each day. Assume the call times are independent.

c)What is the approximate probability that the total time spent on the calls will be greater than 140 minutes? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question. .

d)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 0.92? Give your answer to four decimal places. Use the standard deviation as you entered it above to answer this question

Explanation / Answer

(c) x = 140, = 1.7 * 82 = 139.4, = 1.2

z = (140 - 139.4)/1.2 = 0.5

P(x > 140) = P(z > 0.5) = 0.3085

(d) z- score = 1.4051

x = + z * = 139.4 + 1.4051 * 1.2 = 141.0861

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