Confused about classical Roman life expectancy According to Wikipedia, the average life expectancy in classical Rome was 30. However, if a child survived to age 10, life expectancy was an additional 37.5 years, totaling 47.5 years. My question is, what percentage of population would have to die before age 10 so that the average life expectancy is 30 years?

We assume, as per your comment, that most of the early deaths were shortly after birth. Let $p$ be the probability of early death. Let $X$ be the lifetime of a randomly chosen newborn.

We are told that $E(X)=30$. We are also told that the conditional expectation of $X$, given the child survived to age $10$, is $47.5$. Then under our assumptions, $$30=E(X)=(p)(0)+(1-p)(47.5).$$ That gives $1-p=\frac{30}{47.5}\approx 0.63$, and therefore $p\approx 0.37$.

One can play around with guesses about the actual mean lifetime given that the child died before the age of $10$. For example, if we replace the estimate we used (all deaths before $10$ occur at age roughly $0$) with say conditional mean is $2$, then we are solving the equation $30=(p)(2)+(1-p)(47.5)$. That gives $p\approx 0.385$.