Calculating Cpi with Miss Rate
I agree with you that you can't figure out effective CPI without knowing the average CPI of the processor. If this is a long-hand assignment, I would use your calculations based on a starting CPI. 

Then if you want a numeric CPI, assume an ideal processor that only takes 1 cycle per instruction, yielding 2.89 CPI. State that assumption in your answer.

Disclaimer: I haven't studied processor performance down at this level in over 20 years, and don't have the references at hand to verify your work.