Expected Value and Standard Deviation for sample Randomly selecting 50 people from a population, 45% say 'YES' and 55% say 'NO'. Assuming that the true percentage of people in the population who say 'YES' is 48%, what is the expected value and standard deviation for the random variable "survey percentage who say 'YES'"?

Before you started the survey, the expected percentage saying YES was $48\%$ and the standard deviation from a sample of $50$ would have been $\sqrt{\dfrac{p(1-p)}{n}} \approx 7\%$.
After the survey, you "know" the percentage of the sample saying YES was $45\%$.  This suggests that $22.5$ people said YES and $27.5$ people said NO.   
