Find the average access time. Note: Show all your work for full credit. $(20$ points$)$

Consider a $3-$level memory hierarchy with an $8$ K upper$-$level cache build inside the CPU and an external $128$ K lower$-$level cache.

Assumptions:

Assume the access times of $15$ and $55$ ns$,$ respectively, and the cost of noncache memory reference is $100$ ns $.$ The upper hit rate is $75\%,$ and the lower level hit rate is $91\%.$