Let $\beta$ follow a random normal distribution with mean $\mu$ and variance $c \cdot \sigma^2$. Let $\gamma$ be similarly distributed with mean $\nu$ and variance $k \cdot \sigma^2$. I need an approximate confidence interval of $$Z = - \frac{\beta} {2 \cdot \gamma}$$ By approximate, I figure we can assume independence, and use our estimates of the data involved, but I am not completely sure how to do it. Will it involve a T-distribution?
The estimates are $\mu = 300, \nu = -5, \sigma^2 = 40000$.
