Question $1$: Cache Performance Analysis

A computer system has a cache with a miss penalty of $100$ cycles and a hit time of $2$ cycles. The

miss rate is observed to be $4\%.$

a$)$ Calculate the average memory access time $($AMAT$)$ for this cache.

b$)$ If we could halve the miss rate by doubling the cache size, what would be the new AMAT?

c$)$ How much does the miss penalty need to be reduced to achieve an AMAT of less than $5$ cycles,

assuming the original miss rate?