# When is the ratio of two normals approximately normal?

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?