$\hat{\beta}_1 \sim N(\beta_1, \sigma^2)$

$\hat{\beta}_1 \sim N(\beta_1, \frac{\sigma^2}{\sum (x_i - \bar{x})^2})$

$\hat{\beta}_1 \sim t_{n-2}(\beta_1, \frac{\sigma^2}{S_{xx}})$

$\hat{\beta}_1 \sim N(0, 1)$