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Answer this question for the following values of the standard deviation of waiting times (in seconds): 10, 20, and 30.

Here the standard error is 3

The critical value for a 95% confidence interval is

The value of the standard deviation is 10

$\begin{array}{c}SE=z_{伪/2}\frac{蟽}{\sqrt{n}}\\ n={z^2}_{伪/2}\frac{{蟽}^2}{S{E}^2}\\ n={1.96}^2脳\frac{{10}^2}{3^2}\\ n=42.68444\\ n鈮�43\end{array}$

Therefore,43 calls should be manually monitored during the next year to estimate the true mean time that callers spend on hold to within 3 seconds with 95% confidence

The value of the standard deviation is 20

$\begin{array}{c}SE=z_{伪/2}\frac{蟽}{\sqrt{n}}\\ n={z^2}_{伪/2}\frac{{蟽}^2}{S{E}^2}\\ n={1.96}^2脳\frac{{20}^2}{3^2}\\ n=170.7378\\ n鈮�171\end{array}$

Therefore,171 calls should be manually monitored during the next year to estimate the true mean time that callers spend on hold to within 3 seconds with 95% confidence

The value of the standard deviation is 30

$\begin{array}{c}SE=z_{伪/2}\frac{蟽}{\sqrt{n}}\\ n={z^2}_{伪/2}\frac{{蟽}^2}{S{E}^2}\\ n={1.96}^2脳\frac{{30}^2}{3^2}\\ n=384.16\\ n鈮�385\end{array}$

Therefore,385 calls should be manually monitored during the next year to estimate the true mean time that callers spend on hold to within 3 seconds with 95% confidence