In a company, how large should the sample be to carry out a study of the average time an employee spends daily on the phone? The result must have a maximum error of 3.2 minutes and 95% confidence. Analysis of a preliminary sample resulted in a standard deviation of 8.75 minutes

To determine the sample size required to estimate the average time an employee spends daily on the phone with a maximum error of 3.2 minutes and 95% confidence, you can use the formula for sample size in estimating a population mean: $$\[n = \frac{{Z^2 \cdot \sigma^2}}{{E^2}}\]$$ Where: $$\(n\) = \text{required sample size}$$ $$\(Z\) = \text{Z-score corresponding to the desired confidence level (for 95% confidence, Z ≈ 1.96)}$$ $$\(\sigma\) =\text{ population standard deviation (8.75 minutes in this case)}$$ $$\(E\) =\text{ maximum error or margin of error (3.2 minutes in this case)}$$ Plug in the values: $$\[n = \frac{{(1.96)^2 \cdot (8.75)^2}}{{(3.2)^2}}\]$$ Now, calculate: $$\[n = \frac{{3.841 \cdot 76.5625}}{{10.24}}\]$$ $$\[n = \frac{{294.33625}}{{10.24}}\]$$ $$\[n \approx 28.73\]$$ Since you can't have a fraction of a person in a sample, you should round up to the nearest whole number. Therefore, the required sample size to estimate the average time an employee spends daily on the phone with a maximum error of 3.2 minutes and 95% confidence is approximately 29 employees.