Questions: Construct the indicated confidence interval for the population mean μ using the t-distribution. Assume the population is normally distributed. c=0.99, x̄=12.1, s=2.0, n=5 (Round to one decimal place as needed.)

Construct the indicated confidence interval for the population mean \( \mu \) using the \( t \)-distribution.

Calculate the critical value \( t_{\alpha/2} \).

Given the confidence level \( c = 0.99 \), the significance level \( \alpha = 1 - c = 0.01 \). The degrees of freedom \( df = n - 1 = 5 - 1 = 4 \). The critical value is calculated as: \[ t_{\alpha/2} = t_{0.005, 4} \approx 4.6041 \]

Calculate the margin of error.

The margin of error \( E \) is calculated using the formula: \[ E = t_{\alpha/2} \cdot \frac{s}{\sqrt{n}} = 4.6041 \cdot \frac{2.0}{\sqrt{5}} \approx 4.1180 \]

Determine the confidence interval.

The confidence interval is given by: \[ \left( \bar{x} - E, \bar{x} + E \right) = \left( 12.1 - 4.1180, 12.1 + 4.1180 \right) = (7.9819, 16.2180) \] Rounding to one decimal place, the confidence interval is: \[ (8.0, 16.2) \]

The confidence interval for the population mean \( \mu \) is \( \boxed{(8.0, 16.2)} \).

The confidence interval for the population mean \( \mu \) is \( \boxed{(8.0, 16.2)} \).