Binomial and Geometric · Challenge problem

A test has $100$ multiple-choice questions with $5$ options each. The teacher wants a pass mark $k$ so that a student guessing on every question passes (scores $k$ or more) with probability at most about $0.001$. Using the normal approximation with continuity correction and $z = 3.09$ for the top $0.1\%$, find the smallest such $k$.