According to a 2018 Rasmussen Poll, 40% of American adults were very likely to watch some of the Winter Olympic coverage on television. The survey polled 1000 American adults and had a margin of error of plus or minus 3 percentage points with a 95% level of confidence. 

a. State the survey results in confidence interval form and interpret the interval.

b. If the Rasmussen Poll was to conduct 100 such surveys of 1000 American adults, how many of them would result in confidence intervals that included the true population proportion?

c. Suppose a student wrote this interpretation of the confidence interval: “We are 95% confident that the sample proportion is between 37% and 43%.” What, if anything, is incorrect in this interpretation?