Suppose that $X \sim N(\mu_1,\sigma_1)$ and $Y \sim N(\mu_2,\sigma_2)$ are two independent normal random variables. Define $Z = X/Y$. I noticed that there are some cases where the distribution of $Z$ is close to normal
set.seed(11) X = rnorm(1000,10,1) Y = rnorm(1000,10,0.1) Z = X/Y hist(Y) shapiro.test(Z)
Questions. When is the distribution of $Z$ approximately normal? Are there any relevant references to justify this approximation?