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'"?
2026-03-31 15:50:47.1774972247
Expected Value and Standard Deviation for sample
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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.