The confidence interval is given by:

$[\hat{\beta} - C_t \times \text{SEE}_{\hat{\beta}}, \hat{\beta} + C_t \times \text{SEE}_{\hat{\beta}}]$

The critical value ($C_t$) at 1% (0.5% on each tail) level is 2.618. (From the standard normal table)

Now, $\text{SEE}_{\hat{\beta}}$ is given by,

$\text{SEE}_{\hat{\beta}} = \sqrt{\frac{s^2}{n \hat{\sigma}^2_X}} = \sqrt{\frac{20.45}{120 \times 18.65}} = 0.0956$

So,

= [1.3997, 1.9002]$$