If we have, $$Z=\frac{X}{Y}$$ where $X$ and $Y$ have different mean and normally distributed.
What is the mean and standard deviation of $Z$. We know, that is a Cauchy Distribution, then $Z$ may be approximately normally distributed. Here is the Jouranl of ratio of normal variable. link
Let $f(z)$ be the PDF of a cauchy, then $$\mu_Z = \int_{-\infty}^{\infty} z f(z) \ dz = \underbrace{\int_{-\infty}^{0} z f(z) \ dz}_{-\infty}+ \underbrace{\int_{0}^{\infty} z f(z) \ dz}_{+\infty}$$ I'll leave the conclusion to you ..