Consider a memory hierarchy system consisting of two levels. The access time of level $1$ is $2$ ns. The miss penalty (The time to get data from level $2$, in case of miss) is $100$ ns.
If the average memory access time is $5$ ns, then in order to reduce the average access time to $40 \%$, the probability that valid data found in level $1$ is ___________ $\%$