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Hi, there seems to be quite a few errors in your copy/pasting of the question, can you make sure it is right?
I assume the probabilities are 30% boom with 15% return, and 70% bust with 3% return.
So the mean return is 6.6% = (0.3*0.15) + (0.7*0.03)
The answer notation is messy too, as the power function is missing.
But in essence the answer is correct where std deviation is 5.5% = [0.30*(0.15 – 0.066)^2 + 0.70 × (0.03 – 0.066)^2]^0.5