Answer: Required 99% confidence interval  : (48.30%, 61.7%)
Step-by-step explanation:
Confidence interval for PROPORTION:   , where p = sample proportion , z* = two-tailed critical z-value  and S.E. = standard error.
, where p = sample proportion , z* = two-tailed critical z-value  and S.E. = standard error.
As per given: p=55%
Critical z-value for 99% confidence = 2.576
S.E. = 2.6% 
Then, required confidence interval :

Required 99% confidence interval  : (48.30%, 61.7%)