To calculate the 95% confidence interval for the mean, we use the formula: $\bar{x} \pm Z_{\alpha/2} \left(\frac{\sigma}{\sqrt{n}}\right)$

Given: $\bar{x} = 130$ $\sigma = 20$ $n = 50$ $Z_{\alpha/2}$ for 95% confidence $= 1.96$

Margin of error $= 1.96 \times \left(\frac{20}{\sqrt{50}}\right) = 1.96 \times 2.8284 \approx 5.54$ The confidence interval is $130 \pm 5.54$, which corresponds to the range$(124.46, 135.54)$. This closely matches option D (124.5, 135.5).