A disk-block cache has the plotted miss rates. Cache read latency is 1 ms and disk read latency 10 ms. Checking presence is negligible. Available sizes are multiples of 10 MB. Find the smallest size giving average latency below 6 ms.
For miss probability m, average service latency is $1(1-m)+10m=1+9m$. Requiring it below 6 gives m<5/9≈0.5556. The graph gives m=0.60 at 20 MB and 0.40 at 30 MB. Thus 20 fails and 30 succeeds with 4.6 ms; minimum 30 MB.
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