The bandwidth of a timed language characterizes the quantity of information per time unit (with a finite observation precision $\varepsilon$). The asymptotic behavior of the bandwidth as $\varepsilon \to 0$ classifies timed regular languages in three classes: meager, normal, and obese. Normal timed automata have a bounded frequency of events and some non-punctual transitions, and, up to now, were the only class of timed automata for which no algorithm was available for computing their bandwidth. In this article, we compute the bandwidth of any such automaton in the form $\approxα\log{1/\varepsilon}$. Our approach reduces this problem to computing the best reward-to-cost ratio in a weighted finite graph constructed from the given timed automaton.