A new microprocessor was designed and tested for performance. This microprocessor requires $2,5$ or $6$ machine cycles to perform various operations. $45\%$ of its instructions take $2$ machine cycles,

$40\%$ take $5$ machine cycles and $15\%$ take $6$ machine cycles.

a$)$ Compute the average CPI for the microprocessor. $[1$ Mark $]$

b$)$ What is the clock frequency required for the CPU to be at $500$ MIPS? $[2$'Marks$]$