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Question 3: The provincial government in Nova Scotia is considering introducing a carbon tax in the province. Past studies show that \( 51.2 \% \) of the Nova Scotians support the tax. (5\%) (a) The provincial government conducted a new survey in 2022 among a random sample of 1,240 respondents. Calculate the probability that majority of the respondents (L.C. more than \( 50 \% \) of the respondents) in the 2022 sample are in favor of the carbon tax assuming that the proportion of the Nova Scotian population that favors this initiative is \( 51.2 \% \). Explain. Draw a graph to illustrate your answer. (5\%) (b) Assuming that the proportion of the Nova Scotian population that favors carbon tax is \( 51.2 \% \), with \( 16 \% \) probability, the proportion of the respondents in the 2022 sample that supports the carbon tax will be less than what percentage? Explain. Draw a graph to illustrate your answer. (5\%) (c) The probability is \( 40 \% \) that the proportion of respondents that favours the carbon tax in your sample will be contained within what symmetrical limits of the true (i.c. population) proportion? Explain. Draw a graph to illustrate your answer.

(a) Distribution of sample proportion: p^ is Normal(mean = 0.512, sd = sqrt(0.512*(1-0.512)*(1/1240)) = 0.01419 ) P(p^>0.50)=1?P(p^?0.50) = 0.8011 R-c

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