Sample size calculation--population is known

Okay, so the goal is to survey...

If you don't know the expect proportion you should take the worse case: Proportion=0.5
confidence level=0.95

sample size=385

This says that if you get the result that 0.5 (50%) of the sample prefer the green color.
The confidence interval will be 0.5±0.05 or 50% ± 5%.
1)Thanks a ton friend.what is the formula you used.

2)Also help me solve my one more query.

i have to upload a excel file with different fields to call the customer for can i prove that my survey is unbiased and random.

I upload the data of total number of repairs done in a week.please suggest,is there any way to prove the data is random like a run test for continuous data.

Also a very Happy New year in advance.!!