A software distributor has opened a new customer call center to assist customers

Question

A software distributor has opened a new customer call center to assist customers with the installation and use of their software. The manager is assuming that the amount of time required to service a customer, X, is a normally distributed random variable. In an attempt to get some information on the population mean service time, , the manager has selected a random sample of 16 calls and found the average service time is 24 minutes with S = 4.2 minutes. The manager would like to take another sample and determine a 95% confidence interval with a half width of the interval (margin of error) of 1.5 minutes. What sample size would be needed to achieve this goal?

Explanation / Answer

From the first sampling, we get s = 4.2minutes

For 95% CI, zcrit = 1.96

Formula for margin of error is ME = zcrit*(s/sqrt(n))
1.5 = 1.96*4.2/sqrt(n)
n = 30.12 = 31(rounding up)

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