A simple random sample of 140 residents in a city was polled the week after the Game of Thrones finale, and 75 of them said they'd watched the finale.  a) Construct a 95% confidence interval for the population of the residents of the city who watched Game of Thrones.  b) Season 7 of Game of Thrones was the third most watched TV program in this city's history, with 48.1% of TV sets in America tuned in. Someone claims that the percentage of people who watched this season in this city was less than 48.1%. Does the confidence interval contradict this claim? Explain. c) Use the results from the sample of 140 to estimate the sample size necessary for a 95% confidence interval to have a margin of error of 0.025.

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