Calculating standard deviation after increasing sample size ?? 10 points BA

A poll of 93 students found that 35% were in favor of raising tution to build a new math building. The standard deviation of this poll is 6%. What would be the standard deviation if the sample size were increased from 93 to 267?

I dont agree that the std dev of the poll is 6%. The std dev of a percentage is sqrt(p (1-p)/n) =
sqrt((.35)(.65)/93) = .049, or 4.9%.

For a sample size of 267 (assuming the same 35% results), would be sqrt((.35)(.65)/267)=.029,
or 2.9%